Crack the eggs into a bowl. Add the shredded cheese, chopped parsley, salt, and black pepper. Whisk until well combined.
Heat a skillet over medium heat and melt a little of the butter. Add the chopped onion and diced bell pepper. Cook for 3 to 4 minutes, stirring, until softened and lightly golden. Remove from the pan.
Cut a hole in the center of each bread slice. Melt the remaining butter in the skillet and place the bread slices in the pan.
Spoon the cooked onion and pepper mixture into the center of each bread slice.
Pour the egg mixture over the bread slices, letting it fill the cutout centers and spread across the tops.
Cook over low to medium-low heat until the egg is mostly set and the underside is golden.
Carefully flip with a spatula and cook the second side until golden and cooked through.