When interpreting any author, it is crucial to understand his terms. Reading The Book on Adler (sometimes titled Concerning Authority and Revelation), I have come to understand that the essentially Christian (which I take to be equivalent to "the essence of Christianity") is a key phrase for Kierkegaard. But what does he mean by this? In which of his books does he discuss what this means? Many people have different opinions on what is the essence of Christianity is, so I cannot assume that Kierkegaard means by this what I would envision by it.
Here is an example use of the phrase in context (The Book on Adler, ed. and tr. Hong & Hong, 116):
Alas, the knowledge acquired for a theological degree—unless one brings along the university from one's childhood and upbringing that which purely religiously is of infinite value: a profound veneration for Christianity so that someday in the later moment of decision one resolutely and with bold confidence stands by the choice, would rather give up everything else than change the least jot in the essentially Christian—alas, the knowledge acquired for the theological degree, even if it could have ever so much worth considered as knowledge, is of but little use in orderly resistance to an emotion that goes to extremes.