On his priesthood, Cohen wrote-
"I knew I wanted to be a priest since I was seventeen and a half. I never saw myself as the kind to plan ahead, but I always knew what I wanted to do, and sometimes I needed to wait. I felt, in every bone in my body, that the best thing I could do was to become a priest, so I set and I waited another year and a half, finished school, volunteered, and finally- started my training. There was no place in Denmark where I could learn what I needed, so I left for Rome. I never liked Rome. It was too hot, humid, and excessively decorated. I would never admit back then, what Catholic priest would stand in front of the Vatican wishing that he was in Copenhagen? I would say it was an early sign, but Jerusalem never impressed me either, so the neutral assumption is that I just love my hometown. Nevertheless, those eight years flew by, and I was over the moon when I boarded the plane back to Denmark, a priest. For the next four, I served as a second priest at the St. Ansgar's Church while I got my teacher's degree. I have thought about becoming a teacher when I was still in Rome, and I believed that I should get all the learning over with quickly, so I could spend the rest of my life helping others instead of learning for my own sake. Teaching fulfilled me, being a priest fulfilled me, I never had any higher aspirations. I was sissified, and I would have stayed in this position for the rest of my life, but the bishop of Copenhagen died. The next bishop needed to be danish, and back then most of the catholic priests in Denmark were foreign, so while all of the bishops of Copenhagen that came before and after me where exceptional man, I find it hard to believe that the bar was very high when I was chosen. That was the first time that life didn't comply with my plans."
Though the limited number of eligible candidates might have played a part in Cohen's election, it seems, at least according to his later accomplishment, that he has underestimated his qualifications.
In his 14 years as a teacher Cohen left a lasting impression on his students. The few that I manage to contact described him as a great teacher, and of course, I would recommend that you read Clara Pedersen's article "My history teacher, John XXIV". Pedersen, a respected danish journalist, is not Cohen's only student to gather an impressive resume. Most interestingly Agner Madsen, who became a member of the swiss guard shortly before John XXIV began his papacy.
After becoming a bishop, no longer being able to teach, Cohen threw himself into charity work, which became his life long passion and a contributing factor to the unfortunate circumstances of his papacy. It seems like he didn't enjoy much of his time as bishop, his writing on the period containing only two sentences -
"Those were ten long years- I did some important work, and I hope I have helped my community, but I constantly felt stuck. Unable to work on the big projects I saw as most important, and unable to dedicate time to teach in a classroom, where I felt most capable to help."
Undoubtedly, the event that sparked the most public interest (both Catholic and non-catholic alike) in David Cohen was his arrival to the bar mitzvah of Ernest Adler's eldest son.
Liking the imagery, Isak Berendsen, a beginning photographer, and Adler's brother-in-law, asked Cohen if he could take a picture of him on a smoke break outside the synagogue. That picture of him- smoking underneath the Hebrew lettering of the synagogue's lintel, in a clerical collar and a red zucchetto (that you might have seen recently in various articles about his Jewishness, or floating out of context around the internet), was shown by Berendsen to a journalist, Terese Hansen, which sparked her interest in the story.
Hansen eventually wrote "Father Cohen- how a Jewish boy became the Catholic bishop of Copenhagen" (translated to English by Chuck Nielsen), a short article, including an interview with Cohen, published in the Berlingske. The beginning of the interview includes a shortened version of the conversion story seen in his records, but I believe we can learn more about his life and personality at the time from this later part of the interview.
"So do you still spend the holidays with the family?
I try to, well, the Seder is a bit difficult for me, but I go every time it falls outside the Holy Week, the High holidays are easier. Obviously, I don't observe any of them, but neither does my family really, they aren't very religious... We always have a great time.
What about Hanukkah?
I try to come for at least one night, can't miss the latkes! (the bishop laughs) I invite them to Christmas too, my brother brings his children, it's very nice to have my family around.
About the photo-
The photo?
The one outside the synagogue
Oh, I was at a childhood friend's son bar mitzvah
You wore a clerical shirt to a bar mitzvah?
I must confess that I don't have any other formal shirts. Becoming a priest straight out of high school saved me the trouble of developing a fashion sense, I gave my friend a choice and he chose the dog collar over the cassock or, and I quote 'one of your hobo shirts'.
And the zucchetto?
Close enough to a yamaka, isn't it? They didn't know the difference."