"Whom do you bless?"
Translation:את מי אתה מברך?
Not a very formal explanation - It is an action you do on someone so you have to use Et.
I don't think it's that מי is indefinite -- rather, it's like asking in English "Who are you blessing," rather than "Whom are you blessing". The את (et) doesn't belong to the מי, if that makes sense -- instead, it follows the מברך.
(I realize you've long moved on and probably speak far more Hebrew than I do at this point; this is for anyone else who comes across it.)
I was taught that את is the marker for a definite direct object. The only thing that resembles a direct object in this sentence is מי. Meanwhile, I'm pretty sure that we don't say את מה אתה רוצה. We say מה אתה רוצה, with no את. The upshot is that, for some obscure reason, מי counts as a definite direct object, but מה doesn't. This doesn't make any logical sense, but there are things in every language that don't make sense. We just have to get used to them.
Yes, it lacks logic, but grammar is not alway logical. Lewis Glinert writes in his Grammar of Modern Hebrew: "Acting as direct object, מי mi 'who' requires the 'direct object particle' את et, ordinarily only found with 'definite' pronouns (eg. את זה et ze 'this'). By contrast, מה ma 'what' takes את et only in 'echo questions, as in רָצִ֫יתִי אֶת זֶה ־ אֶת מָה? 'I wanted this. - You wanted what?".
I'm a bit salty because I did the feminine version, "את מי את מברכה?" and it told me that I had "typos in [my] answer" and 'corrected' it to the male version (את מי אתה מברך). It wasn't wrong... just feminine.