Fatuously is how you do something when it is empty-headed and a little smug. You use it of talking, smiling, grinning, or nodding — the way a person behaves when they look sure of themselves and have not really thought. It is the adverb of fatuous, so it has the same rather bookish, slightly sharp feel. You are more likely to read it than hear it at the dinner table. Though actually, it does more than say “in a stupid way.” Stupid can be clumsy or slow; fatuously points at a kind of cheerful emptiness, as if the speaker is pleased with a thought that has no weight.

愚昧可笑地