Preheat the oven to 400 degrees F (200 degrees C). Line 2 baking sheets with parchment paper.

Heat a large skillet over medium-high heat. Cook and stir sausage in the hot skillet for about 3 minutes. Add onion and continue cooking until sausage is browned and crumbly, about 3 minutes more. Drain and discard grease.

Add 3/4 of the Cheddar cheese, apples, and rice to the sausage in the skillet. Beat 1 egg in a bowl and add to the skillet. Mix well; add salt and black pepper.

Unroll 1 sheet of puff pastry on the prepared baking sheet. Sprinkle 1/2 the remaining Cheddar cheese down the middle and top with 1/2 the meat mixture. Cut the sides of the pastry into strips and braid them together over the filling. Pinch ends to close. Repeat with remaining puff pastry, cheese, and meat mixture.

Beat remaining egg in a bowl and brush onto both stuffed pastries.

Bake in the preheated oven until golden brown, 30 to 40 minutes.