Heat oven to 350F/175C. Grease a 9x13-inch (23x33cm) baking dish with the butter.

Whisk the 12 eggs with 3 tbsp milk, 1/2 tsp salt, and 1/4 tsp black pepper in a mixing bowl until smooth. Pour into the prepared dish.

Bake for 20 to 22 minutes, until the center is fully set and no longer jiggles when you shake the pan. Cool in the dish for 5 minutes, then cut into 6 rectangles about the size of the English muffins.

While the eggs bake, divide the 680 g (1.5 lb) bulk breakfast sausage into 6 patties, about 113 g (4 oz) each, pressed 1/2 inch thick and slightly wider than the muffins since they shrink as they cook.

Heat the 12-inch cast iron skillet over medium heat. Cook the patties in two batches of 3 so they aren't crowded, 4 to 5 minutes per side, until an instant-read thermometer reads 160F/71C and there's no pink in the center.

Split and toast the English muffins until golden at the edges.

Lay a slice of cheddar on the bottom half of each warm muffin so it starts to melt, then add a sausage patty and an egg rectangle. Close with the muffin top.

Cool the assembled sandwiches completely on a wire rack, about 15 minutes, before wrapping. Wrapping them warm traps steam and makes the muffin soggy once frozen.

Wrap each sandwich tightly in foil or parchment, then place in a freezer bag or airtight container. Freeze for up to 3 months.

To reheat from frozen, unwrap and microwave on 50% power for 90 seconds, then full power for 30 to 45 seconds, until hot in the center.