"All our X" vs. "all of our X"

Solution 1:

Both sentences are grammatical.

See the following NGRAM (all our, all of our):

It would seem that the use of "all of our" is growing nowadays.

Also, "all of our" ("all of our delicious") gets 18,200,000 (745) hits on Google Book, while "all our" ("all our delicious") gets 26,500,000 (4,240) hits.

Solution 2:

If you go back a century or so, "all of" would be very rare indeed. The fact that it occurs a bit more often nowadays is no real reason for using it - it's still far more common not to use "of" after "all".

Having said that, in OP's context either form is acceptable. For reasons that aren't clear to me, it seems that "of" is actually required when followed by a pronoun...

You took the part that once was my heart. Why not take all of me?

My father won eight thousand dollars the night before, but lost all of it last night.

I can't think of any similar context where including the preposition is "unacceptable", though it would certainly be stylistically clumsy to overdo it...

"You can fool all [of] the people some of the time, and some of the people all [of] the time, but you cannot fool all [of] the people all [of] the time." (attrib. Abraham Lincoln, among others).

Idiomatically, all is slippery. You can take all of me/it/us/them, and you can take it/us/them all, but you can't take me/him/her all. That's not because those pronouns are singular (take it all is unremarkable) - it's just a matter of idiomatic usage.