Adjust heat to maintain a simmer, as needed. Toast muffins under broiler about 2 minutes until lightly browned. Transfer muffins to a plate and top with bacon. Remove eggs from water with a slotted spoon. Hold spoon against a clean dishtowel to drain.
Place eggs over bacon.
Top with hollandaise sauce. Sprinkle with finely chopped parsley and paprika, if desired, and serve immediately. Combine egg yolks, lemon juice, salt and cayenne in blender. Quickly turn blender on and off. Melt butter in microwave or on stovetop until it is bubbling but not browned.