Set your oven to 450 degrees or broiler to high.
Heat 1 tbsp of butter in Small Fry (or another skillet) and cook eggs over medium-high heat, being sure to cook eggs to the left or right of pan. Allow the eggs' edges to get crispy and the bottoms of the yolks to just set.
Gently flip the eggs and cook for another 1–2 minutes, or until the yolks are soft to the touch. Season generously with salt and black pepper.
While the eggs are cooking, use the other side of your pan to crisp the stuffing. Form the stuffing into a patty the same width as the English muffin. Dust both sides of the patty with AP flour (rice flour works, too, and is gluten-free). Lay your stuffing in the pan with the remaining butter and let sizzle until the edges are golden brown. Flip and repeat with the other side.
Remove from heat and drain on a paper-towel-lined plate. Lightly toast the English muffin.
To assemble, place the stuffing patty on the bottom half of the English muffin. Smear with half of the cranberry sauce, then top with eggs and chopped turkey. Finish with the cheese, and bake in the oven until the cheese just starts to drip down the sides. Spread the remaining cranberry sauce on the top half of the English muffin.
Separately, heat the gravy and serve in a bowl on the side, for dipping.