In a large skillet over medium-high heat, cook the ground sausage until browned. Add diced onion and cook until softened. Drain any excess grease.

In a bowl, whisk together 8 eggs, salt, and pepper. Pour into the skillet with the sausage. Scramble until the eggs are just set. Remove from heat and stir in the shredded cheese. Let the filling cool.

Preheat your oven to 400°F (200°C). Roll out the dough on a floured surface and cut into 8 equal rectangles.

Spoon the cooled filling onto one half of each rectangle, leaving a border. Brush the edges with water.

Fold the dough over the filling and press the edges with a fork to seal tightly. Place on a parchment-lined baking sheet, brush the tops with the beaten egg wash, and cut a small slit in the top of each. Bake for 15-20 minutes, or until golden brown.