in a large skillet over medium heat, lightly brown bacon (about 3 minutes per side). remove from skillet and keep warm.

fill a medium skillet half full of water. bring to a boil, then reduce heat to simmering. break 1 egg into a small dish, then slide egg into simmering water. repeat with remaining eggs. simmer eggs, uncovered, for 4 to 5 minutes, until yolks are set, but not hard.

meanwhile, in a small saucepan, whisk together mayonnaise, sour cream, honey mustard, lemon juice, salt, and cayenne. cook over medium heat just until mixture is heated through. do not boil. remove sauce from heat.

for each serving, place 1 toasted english muffin-half on a plate. top with 2 slices bacon. remove 1 egg from water using a slotted spoon. place egg over bacon. pour 2 tablespoons sauce over egg, garnish with fresh dill or parsley, if desired. serve immediately.