In a large bowl, combine the beef, Worcestershire, Dijon and horseradish; season with salt and pepper. Shape into 6 patties. Heat a griddle or cast-iron skillet over medium-high. Cook patties, turning occasionally and basting with melted butter, about 8 minutes for medium-rare. Top with slices of cheddar and cover for the last minute or two of cooking until the cheese melts.
For the mayo, in a medium bowl, whisk the egg yolk, Dijon and lemon juice; then, continuing to whisk, slowly stream in the oil, letting it pour down the sides of the bowl. Season with sea salt.
For the aioli, in a medium bowl, mix the mayo, blue cheese, parsley, Dijon and garlic.
Divide the cheeseburgers among the roll bottoms; spread the aioli on the roll tops. Top the burgers with lettuce, tomato, onion and the roll tops.