In a large skillet over medium heat, cook the breakfast sausage until browned and crispy, about 6–8 minutes.

Sprinkle in 2 tablespoons of all-purpose flour, stirring for about 1 minute until absorbed, then whisk in 1 cup of whole milk and cook for 3-4 minutes until thickened.

In a non-stick pan, scramble 4 large eggs over medium heat until fluffy, about 3-4 minutes.

In a bowl, combine 2 cups of all-purpose flour and 1 teaspoon of salt. Cut in ½ cup each of vegetable shortening and butter until resembling coarse crumbs. Whisk one egg, 1 tablespoon of vinegar, and 6 tablespoons of cold water, then blend into the flour mixture.

Roll out the dough to about ¼ inch thick and cut into rectangles measuring 3x4 inches.

Preheat the oven to 375°F (190°C) and line a baking sheet with parchment. Brush edges of half the rectangles with egg wash, add sausage gravy, scrambled eggs, and cheese, then top with another rectangle and crimp edges.

Brush the tops with egg wash, sprinkle with salt and pepper, and bake for about 25 minutes until golden brown.

Let cool for 5 minutes and serve warm.