A girl that I like frequently calls me 笨蛋. I want to confess my feelings to her and wasn't sure if saying 我知道我很笨蛋。 or 我知道我是笨蛋。makes more sense gramatically.
我知道我很笨，…… [很 + adjective]
我知道我是（个）笨蛋，…… [是 + noun]
Presumably you'd want the latter to echo your romantic interest's wording.
I don't believe it's grammatically correct to say 我很笨蛋 since 很 would normally be followed by an adjective (or something functioning as an adjective).