Dear reader, please keep in mind that this is only the prologue to give background information, so there are certain structure issues. In the actual episodes, there will be much more organization with dialog and fighting. So without further ado:
Before the events of Dragon Ball Z (756), Broly wanted to have a son whom would be the heir of his universal empire he "knew" he would some day rule over. Broly decided to go back in time by forcing an intelligent scientist to build him a time machine and he would kidnap Goku's mother moments before Planet Vegeta blew up and take her back to his time. He had his way with her and kept her a secret from his father, Paragus, who found out about her when he caught her giving birth one day while Broly was away. Immediately, Paragus wanted to get rid of Broly Jr. because he knew how unruly Broly was and did not want to have to deal with another uncontrollable beast. So Paragus decided to kill both the mother and the baby. But as he was killing the mother, Broly Jr. incidentally crawled into a space pod and pressed buttons playfully when it suddenly shot off into space. Paragus was furious, but knowing the child had no destination and only an hour worth of life support left- he trusted Jr. would die soon enough. When Broly came back, Paragus made up a story that the baby was acting mad with rage and even killed the mother so Paragus was forced to kill him. Coincidentally, half way across the universe, this was the same day Chi-Chi was giving birth to Goku's first child, Gohan.
Meanwhile, as the baby aimlessly flew through space, Grand Kai had his eye on the small warrior. After all, Grand Kai had been watching the whole story unfold and was interested in what would happen. Knowing the potential of Broly Jr., and not wanting to just leave a baby to die, Grand Kai secretly took Broly Jr. under his care, raising him as his own with the plan of taming him and turning him into his star pupil. In an attempt to make sure no one would find out who Jr's father was, Grand Kai renamed him Brocc (still a pun off of broccoli).
Expectedly, Brocc was quite unable to be tamed and so Grand Kai had to resort to drastic measures. He had to gain trust from the savage the only way Brocc knew of: he helped the child in desperate times. When Brocc would go on a raging fit- Grand Kai would have him put in a special Hyperbolic Time Chamber (one where people can go numerous times). Minutes later (in outside-world time, which is many hours later in the HTC), after Brocc would grow weary, Grand Kai would then send in a strong warrior to beat the infant until he passed out. Once that was done, Grand Kai would get Brocc and nurture him back to health personally. This would help Grand Kai gain Brocc's respect, and Brocc would also get stronger through this process. Soon enough, Brocc looked at Grand Kai as his own father, who then took that opportunity to teach nothing but purity and kindness to Brocc is hope of him growing up into a peaceful man.
By the time Brocc turned 5 years old (4 years time, but time spent in HTC added up is 1 year), Grand Kai had taught him the fighting basics like flight, energy barrier, and sensing energy levels, among many other abilities. Grand Kai would insist on making Brocc only train in Kaioken to further intensify his training. That is, of course, until Brocc reached Super Saiyan levels. By the time Brocc turned 11, he was training as a Super Saiyan 2, and Grand Kai had taught him such things as instant transmission, and Kairate (pun off of Karate), a martial arts that was specifically designed by Grand Kai for fights that involve ki attacks. Also, Grand Kai instructed him on ways of powering-up attacks faster than usual by using special meditating techniques before battle and therefore have more inner ki at the literal tips of his fingers. Because of that lesson, he had learned some more powerful versions of well-known techniques, like Megameha, which is a more powerful and quicker version of the Super Kamehameha. Grand Kai even taught Brocc how to do the Ki Missile, a more powerful form of Spirit Bomb that is super-condensed into the user's hand. It was only once Grand Kai was sure that he could trust Brocc that he revealed what Oozaru was and how to create a "fake moon" in order to transform into Oozaru.
Time goes by and Grand Kai decides to finally tell the now 18 year old Brocc (774), who could reach Super Saiyan 3, about his father, Broly, and showed him a recording of what happened. Luckily, Brocc took it well because he looks up to Grand Kai as his real father instead. After that, in early September, Grand Kai chooses to let Brocc leave to explore the universe, telling him, "Your training is complete."
Dear reader, thanks so much for viewing my FanFic! Now let me just point out a few things that I may not have been clear enough about:
So Brocc was conceived on August of 756, and born on May 26th, 757.
May 26th, 757 is the same day that Gohan was born, so Gohan and Brocc are the same age. This is even true when you calculate the HTC because both of their bodies have spent a year's worth in them.
Goku destroys Kid Buu in early May 774, making Gohan and Brocc's bodies both 17 years old (although in only 16 years time), and then the 26th of May comes by and they're both 18 years old.
Grand Kai lets Brocc go travel the universe on September 8th 774, the day after Shenron erases everyone's memories of Majin Buu.
Let me know what you thought!!!