Place 4 slices of bread on a work surface. Cover evenly with cheese slices and arrange the mushrooms and green onions over the cheese. Season to taste with cayenne.
Cover with remaining bread slices to make sandwiches.
Heat a large non-stick skillet over medium heat. Add half the oil.
Place the sandwiches in the skillet, then cover them with aluminum foil, place a weight on top of the foil, and continue cooking until the first side is golden and crisp. Turn the sandwiches, add the remaining oil and repeat the process.
To serve, cut each sandwich into four triangles and garnish with a skewer of condiments.