For the maple hot butter: Melt butter in a small saucepan over medium-low heat. Whisk in the maple syrup and hot sauce. Keep warm.
For the burgers: Combine the sausage, beef, parsley, 1 teaspoon salt and 1/2 teaspoon pepper in a mixing bowl. Use your hands to divide the meat into four 4-ounce balls.
Place a large cast-iron griddle over medium-high heat until warm, then add butter to grease the griddle. Place the balls of meat on half of the griddle and smash into round patties, about 4-inches wide, using a flat spatula. Fry until evenly browned, 3 to 4 minutes per side. Lay a slice of cheese over each patty. Invert a metal bowl over the patties to melt the cheese until it fries into crispy lace on the sides of the burgers, about 2 minutes.
For the French toast buns: Meanwhile, whisk together the cream, milk and eggs in a bowl. Soak the potato buns briefly in the mixture, about 20 seconds per half.
Place on the other half of the griddle (you may have to do this in batches) and griddle until golden brown and cooked through, about 2 minutes per side. Remove to a plate and drizzle with the maple hot butter, reserving some for the patties.
Place avocado slices on the bottom French toast buns, then top with cheesy patties. Drizzle the remaining spicy maple butter over the patties. Top with the remaining French toast buns and serve immediately.