I haven't watched all of azumanga_daioh or read any of the 4koma, but it's pretty likely that this is a reenactment of an azumanga scene. Notice that Zekeltarfos added "parody" and "azumanga_daioh" at the same time (look at the tag history).
You like sweet things, right?Oh!S-say that again.Huh?M-more, more!Like, like.Like. I love them-ze.I like them, ze. This could also mean "I like you" (though it clearly doesn't, in context), hence Alice's reaction.Ice cream! I bought both vanilla and chocolate!