This seems not a question but what is it?

Question

"And if I find you have broken your promise to me and to God, I will reveal your crime to your victims."
   "And they will kill me. Good work, Father."
   "As far as I can see, it's the best way out of a moral dilemma. And my priest agrees. So take it or leave it."
   "I have no choice."
   "God bless you, my son," said Spirya.
   Lev walked away.
   He left the grounds of Ty Gwyn and headed through the rain back into Aberowen, fuming. How like a priest, he thought resentfully, to take away a man's chance of bettering himself. Spirya was comfortable now, food and clothing and accommodation all provided, forever, by the church and the hungry worshippers who gave money they could not afford. For the rest of his life, Spirya would have nothing to do but sing the services and fiddle with the altar boys.
(Ken Follett, Fall of Giants)

The clause seems not a question for there’s no question mark. And so I imagine a parsing: “how like a priest” is “what a (darn) priest” and to infinitive is the reason for the previous part. How do I understand it?

Answer 1

It's not a question at all, in fact.

"How like an apple, to be round and red."

"How like (something)" is used to mean something adheres to what is expected.

I.e. "The apple is red and round, like apples tend to be."

It means the priest's actions were normal and average for his occupation, at least from the speaker's perspective. In this case it is used derisively, in a cynical way.

Answer 2

This is an exclamative clause. An exclamative clause contains an exclamative phrase which in turn contains what or how. In this case our exclamative phrase is how like a priest. When the exclamative phrase doesn't contain the subject, it must be fronted; otherwise, it stays where it is.