Preheat your oven to 350°F (175°C).

In a large skillet over medium heat, cook the bacon until crispy. Remove from the skillet and let drain on paper towels. Reserve about 1 tablespoon of bacon grease in the skillet.

In a bowl, whisk together the eggs, milk, salt, and pepper. Pour the egg mixture into the skillet with the reserved bacon grease. Cook over medium heat, stirring gently until the eggs are scrambled and just set, about 5-7 minutes.

While the eggs are cooking, slice the slider buns in half and place the bottom halves in a baking dish.

Layer the cooked bacon on the bottom halves of the buns, followed by the scrambled eggs, and then top each with a slice of cheddar cheese.

Place the top halves of the buns on the sliders. Melt the butter and brush it over the tops of the 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 5 minutes, or until the cheese is melted and the buns are golden.

Remove from the oven, garnish with chopped chives if desired, and serve warm.