Preheat your oven to 325°F (165°C). Split English muffins in half, butter each half, and arrange cut side up on a lined baking sheet.

In a large skillet, heat breakfast sausage over medium-high heat until browned and cooked through. Remove sausage from skillet, leaving drippings.

Reduce heat to medium and add butter to the drippings. Whisk in flour, cooking for 2 minutes. Gradually pour in milk while whisking. Cook until thickened, season with salt and pepper.

Toast the muffin halves in the preheated oven for about 10 minutes until golden and crisp. Remove and let rest.

Whisk eggs with a splash of milk, salt, and pepper. Cook in a non-stick skillet with melted butter until softly scrambled.

Assemble by spooning gravy over each muffin half, adding sausage, scrambled eggs, and topping with cheddar.