First cook the sausage. Cut the sausage casing and remove the meat from the casing. Crumble the sausage and then place it in a small skillet. The sausage should be fatty enough that you don't need to use any oil in the pan. Use a wooden spoon to stir the sausage and break it up into smaller pieces.
While the sausage is cooking, slice the bell peppers in half, and remove the seeds and membranes. Be care not to poke any holes in the peppers, since that would result in the egg white spilling out of the pepper (and you don't want that).
Then pour the water into a large skillet. Place the peppers in the skillet inside facing down, and cook on medium low heat for 4 minutes.
After 4 minutes, use tongs to flip the peppers and season them with a bit of salt and pepper. Divide the sausage and cheese between the four pepper halves. Use a spoon to press the sausage and cheese into the peppers, making room for the egg. You can either crack the eggs directly into the peppers, or crack them into a small bowl first to ensure that you don't accidentally get any egg shell in the peppers.
Cover the skillet and let the eggs cook for 5 minutes, or until the white is solid and the yolk is runny. Serve immediately.