Preheat the oven to 350°F (175°C). Grease a 9x13-inch baking dish.
In a large skillet, cook the breakfast sausage over medium heat until browned and cooked through. Remove the sausage with a slotted spoon and set aside, leaving the grease in the skillet.
In a medium bowl, whisk together the eggs, milk, salt, and pepper. Pour the egg mixture into the skillet with the sausage grease and cook over medium heat, stirring occasionally, until the eggs are scrambled and cooked through.
Split the slider buns or dinner rolls in half and place the bottom halves in the prepared baking dish.
Spread the cooked sausage evenly over the bottom halves of the buns.
Pour the scrambled eggs over the sausage, spreading them out evenly.
Sprinkle the shredded cheddar cheese and Monterey Jack cheese over the scrambled eggs.
Drizzle the barbecue sauce over the cheese.
Place the top halves of the slider buns over the cheese and barbecue sauce layer.
Brush the melted butter over the tops of the slider buns.
Cover the baking dish with aluminum foil and bake in the preheated oven for 10 minutes. Remove the foil and bake for an additional 10-15 minutes, or until the cheese is melted and the sliders are heated through.
Garnish with sliced green onions and serve hot.