Melt the butter in a dish in the microwave. Separate the eggs into yolk and whites. Discard the whites.
In a blender, put the yolks, lemon juice, salt and cayenne pepper and let sit until room temperature. Turn on the blender for 1 min. Very slowly, add a tablespoon of the bowling butter from the microwave. Blend again for another minute. Then add another tablespoon of bowling butter. Do this about 3-4 times, then you can start increasing the butter more and more. Watch the sauce and verify that it's thickening.
If it refuses to thicken, then the butter was added too fast or it wasn't boiling butter, so restart (sorry!).
Serve over english muffins layered with ham and poached or boiled/sliced eggs. Use all the sauce, as if you microwave it, you'll get scrambled eggs.