Doya-gao (ドヤ顔) is a facial expression conveying a self-satisfied, cocky, or smug attitude. To enhance the comedy effect, one may use this expression on a character who is overly proud of something they failed at, or that they have no reason to be proud of.
Doya probably comes from Kansai Japanese "Dou ya?" meaning asking someone "How well am I doing?". The phrase carries an inside meaning of "I looked cool just now, didn't I?"
A few trademarks of doyagao are a cocky expression, featuring a tight closed-lip smile, closed or sparkling eyes, v-shaped eyebrows, and a proud huff, along with hands on one's hips or chest, and a general air of "I totally nailed it just now", when the character didn't nail it at all.