Preheat your oven to 350°F.
In a skillet over medium heat, cook the bacon until crispy. Remove and drain on paper towels. Leave 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 bacon grease and scramble until fully cooked. Remove from heat.
Slice the slider buns in half and place the bottom halves in a greased baking dish.
Layer the cooked bacon on the bottom halves of the slider buns, followed by the scrambled eggs, and then sprinkle the shredded cheddar cheese on top.
Place the top halves of the slider buns on the cheese. Spread the butter over the tops of the buns.
Cover the baking dish with aluminum foil and bake for 15 minutes. Remove the foil and bake for an additional 5-10 minutes, or until the cheese is melted and the tops are golden brown.
Remove from the oven and let cool for a few minutes. If desired, sprinkle with chopped chives before serving.