Preheat your oven to 400°F (200°C) and line a baking sheet with parchment paper.
In a large mixing bowl, combine the flour, baking powder, salt, garlic powder, and onion powder.
Add the cold, cubed butter to the flour mixture and use a pastry cutter or your fingers to blend until the mixture resembles coarse crumbs.
Pour in the milk and stir until just combined. Do not overmix.
Fold in the shredded cheddar cheese, cooked sausage, green onions, and black pepper until evenly distributed.
Turn the dough out onto a floured surface and gently knead it a few times until it comes together.
Roll the dough into a rectangle about 1/2 inch thick. Cut into squares or rectangles, about 3 inches wide.
Place the rolls on the prepared baking sheet, leaving space between them.
Beat the egg in a small bowl and brush the tops of the rolls with the egg wash.
Bake for 15-18 minutes, or until the rolls are golden brown.
Let cool slightly before serving.