It is a normal cap shaped like a Krabby Patty. There are buns with sesame seeds both on top and the bottom of the patty hat. A meat patty lies on the center with some lettuce.
Thaddeus is seen wearing the hat. He says "I wear it cause I'm bald." When Mr. Krabs flies out of the Krusty Krab, Thaddeus bows his head and then takes off his hat to take a bite. The Hatty Patty was also the idea of Squidward, and Mr. Krabs makes it.