Heat the oven to 350°F and arrange a rack in the middle.

Coat 4 6-ounce ramekins with butter and place them on a baking sheet; set aside.

In a medium frying pan, melt the measured butter over medium-low heat until foaming.

Add the bangers and water and cover with a tight-fitting lid. Cook, turning the sausages occasionally, until the water has evaporated and the bangers are browned on both sides and cooked through, about 15 minutes.

Transfer the sausages to a cutting board, let cool slightly, and chop into medium dice.

Evenly distribute the banger pieces among the ramekins.

Break 2 eggs into each ramekin (be careful not to break the yolks), season with salt and pepper, and top each with a quarter of the cheese.

Bake until the eggs are set, or to your desired doneness (18 to 22 minutes for runny yolks).

Remove from the oven and let sit for 3 to 5 minutes before serving.