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 tightfitting 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 (being 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.