Preheat the oven to 350 degrees F. Grease 4 large muffin tin holes with melted butter or vegetable oil.
Heat a non-stick pan over high heat. Add bacon and fry until lightly browned. Remove onto a paper towel to drain the fat.
Place the flour, baking powder, and baking soda in a bowl, and mix to combine well.
Whisk together the buttermilk, salt, sour cream, vegetable oil, and one of the eggs, in a separate bowl.
Pour the wet ingredients into the dry ingredients until just combined. Do not overmix.
Fold in the bacon, scallions, and Cheddar cheese.
Place 3 tablespoons of the batter into 4 muffin tin holes. Bang the tin on the counter to flatten the batter. Make a divot in the batter and crack an egg into each hole. Divide the remaining batter between each muffin hole to cover the egg.
Brush the muffins with the melted butter, than bake for 20 minutes, until golden brown.
Remove from the oven and allow to rest for 4 minutes before turning out onto a cooling rack.