Prepare the Hollandaise Sauce

1. Melt butter in a small saucepan until hot.
2. Place egg yolks, lemon juice, a pinch of salt and cayenne (if using) in a blender or container suitable for an immersion blender.
3. With blender running, slowly stream in hot melted butter until sauce is smooth and thickened.
4. If sauce is too thick, blend in 1 to 2 Tbsp of warm water until desired consistency is reached.
5. Season to taste with salt.
6. Cover and keep warm until serving.

Prepare the Lamb Cutlets

1. Remove American lamb meat from the bone. First cut into individual chop, then slice along the bone by cutting along its length.Slice each piece into ½" thick cutlets.
2. Place cutlets between two sheets of plastic wrap and pound to about ⅛ to 3/16" thickness.
3. Season both sides with kosher salt and pepper.
4. Set up three shallow bowls: one with seasoned flour, one with beaten egg mixed with 1 Tbsp water, and one with breadcrumbs.
5. Dredge each cutlet first in flour, then egg wash, then breadcrumbs. Place on a plate or sheet pan.
6. Heat a 12" heavy-bottomed skillet over medium-high heat. Add oil, then butter.
7. Fry the cutlets for about 1 minute per side until golden brown.
8. Transfer to a wire rack and immediately sprinkle with salt and a squeeze of lemon juice. Keep warm.

Poach the Eggs

1. While preparing the lamb, bring a pot with 4 to 5 inches of water and 1 Tbsp vinegar to a gentle simmer.
2. Crack each egg individually into a fine mesh strainer to drain off excess white, then transfer to a small ramekin.
3. Reduce heat so the water is just barely simmering.
4. Gently slide each egg into the water and poach for 3 minutes.
5. Remove with a slotted spoon and place on a paper towel to drain off any water.

Assemble

1. Place toasted English muffin halves on warmed plates.
2. Top each half with a lamb cutlet.
3. Place a poached egg on each cutlet.
4. Spoon hollandaise sauce over each egg.