Place the bacon in a skillet and cook over medium heat until evenly browned and crisp. Remove, and drain on paper towels. When cooled, crumble into small pieces.
Stir the eggs and 1/4 cup Cheddar cheese together in a bowl until blended. Season to taste with salt and pepper. Pour the egg mixture into a skillet over medium heat. When the bottom of the eggs is set, layer with the bacon, ham, and if using, onion, chives, mushrooms, green pepper, jalapeno or hot pepper sauce. . Season with hot pepper sauce, if desired. Sprinkle with the remaining 1/4 cup Cheddar cheese. Carefully fold one half of the egg mixture over the filling ingredients. Cook until the cheese melts and the bottom is golden; turn and cook the other side until golden. Remove from the heat.
Set two slices of toast on two serving plates, and spread each slice with mayonnaise, if desired. Cut the egg mixture in half, and place one half on each piece of toast. Top each with the remaining toast, cut each omwich in half, and serve immediately.