Line a baking sheet with parchment paper. Place leftover stuffing in a mixing bowl. Stir in beaten egg until evenly combined.
Scoop 1/2 cup of mixture up and form a patty. Place patty on the parchment lined baking sheet. Repeat 3 more times until you have 4 patties.
Place baking sheet in the freezer and freeze for at least 1 hour.
Heat oil in a large skillet over medium-high heat. Place patties in the skillet and cook, undisturbed, for 5 minutes. Carefully flip and cook 5 minutes more or until desired browning is achieved.