My opinions:
1) Eliminate the first sentence. You don't need to begin with "In this brief essay..." (Ugh; everyone already knows this is a brief essay. Moreover, your concluding statement explains why you wrote the essay). "Before my last semester at Columbia University, I was disappointed with the entrepreneurial programs offered in the Engineering school," now THAT'S an opening that captures interest! "In this brief essay, I explain why I chose Prof. <PERSON> as a recommender," is not. General advice: make sure your opening words don't elicit a yawn.
2) "I felt that New York City, and particularly Wall Street, was strongly influencing the culture in the school." The previous sentence has "was" as its verb. This sentence makes two in a row. How about, "I felt that New York City, and particularly Wall Street, held strong influence over culture in the school." General advice: avoid passive voice.
3) "We started by interviewing 30 engineering students and chatting with 12 faculty professors, and soon enough formed a student executive board." "Soon enough formed"? Why not just "soon formed"? General advice: eliminate superfluous words.
4) "Of all the board advisers, I believe that Prof. <PERSON> was the one with the most unbiased and sound guidance. So much so that after my program finished, I have got back to him for career advice. You were on a roll, until you got to this paragraph. 873
Strike the "I believe that..." - be bold enough to make an assertion, even if it's based on personal opinion. Take out the passive voice. And eliminate the weak "so much so..." "Of all the board advisers, Prof. <PERSON> provided the most sound and unbiased guidance. I was very impressed, and have continued to seek career advice from Prof. X. General advice: don't be apologetic about forceful assertions.
5) "I decided to ask Prof. <PERSON> for a recommendation letter because of two reasons:" Change to "I asked Prof. <PERSON> for a recommendation letter for two reasons:" General advice: to write concisely, learn to recognize - and eliminate - unnecessary wordiness.
6) "a vision I was really passionate about" - passive voice, ending with a preposition? I think you can do better than that. General advice: when you spot something weak, don't be content until you've fixed the problem.
P.S. Read How to Say Nothing in 500 Words by <PERSON>. He'll give you the same advice, in a much more entertaining way. 487