Preheat oven to 450°F. Line a baking sheet with parchment paper or a silicon baking mat. Set aside.
Combine flour, baking powder, and salt in a large bowl and mix well. Add the butter to the flour mixture and cut with a pastry cutter until it resembles coarse cornmeal. Make a well in the middle of the mixture. Pour in 1/4 cup of milk. Lightly and quickly mix with a fork. Add additional milk just to form dough moist enough to leave the sides of the bowl and cling to the fork.
Turn dough out on a floured surface. Knead together 4-5 times, adding enough flour to make it less tacky.
Pick up side of dough furthest from you and fold toward you. With palms, push down, pressing dough away from you. Turn dough a quarter turn. Repeat process 6-7 times, working gently.
Lightly roll dough out from the center to 3/4” thick.
Using a floured 3” biscuit cutter, cut out biscuits - straight without twisting - as close to each other as possible. Flour cutter between cuttings. Lift the biscuits with a spatula and place on the baking sheet, about 1” apart. Brush tops of biscuits with milk or melted butter.
Bake 12-15 minutes or until lightly golden. Remove from the oven and set aside to cool slightly.
While baking the biscuits, fry the bacon in a frying pan over medium heat until crispy, about 6 minutes. Transfer bacon to a plate. Remove excess bacon grease from pan. Return to heat.
Crack eggs in the four corners of the pan. Turn down heat if they start to bubble. Fry gently until edges firm up. Carefully flip. Season with salt, pepper, and top with cheese. Continue cooking 3-4 minutes, until yolk is as firm as you like it.
Cut the biscuits in half. Top with the egg, 2 strips of bacon, and the top of the biscuit.