Chop mushrooms and onion. Slice tomato.
Preheat a nonstick skillet over medium heat.
Add chopped onion to hot skillet and cook for 3-4 minutes until softened.
Whisk eggs together with the mushrooms, then add to the onions.
Allow eggs to cook until no longer runny, stirring occasionally to slightly scramble. Once the eggs become firm, do not stir. Flip them over once to fully cook both sides.
While eggs cook, preheat sandwich press or a large skillet.
Divide cooked eggs equally among 4 slices of bread; top each with a tomato slice, a sprinkling of cheese, and then a second slice of bread.
Place sandwiches into the press (or skillet) and cook until cheese is melted and bread is golden on both sides. (If you don't have a sandwich press, then press sandwiches down in the skillet with a small sauce pan while cooking, flipping halfway through to evenly brown both sides.)
Serve with clementines on the side.