Lightly grease six muffin cups with the butter. In a large skillet, cook the bacon over medium heat until cooked but not crisp. Drain on paper towels.
Cut six bacon strips on half width-wise; line the bottom of each muffin cup with two bacon pieces. Line the sides of each muffin cup with one or two bacon strips. Break an egg into each cup. Bake, uncovered, at 325 degrees F for 12-18 minutes or until whites are completely set and yolks begin to thicken but are not firm. Transfer to a serving plate; surround with parsley.