In a skillet over medium-high heat, add 2 teaspoon of oil. When the pan is hot, add the onions and 1/2 teaspoon of salt. Cook until softened and dark brown in color. Halfway through cook time, turn down the heat to medium. Caramelizing onions will take about 20-30 minutes; if the pan is getting slightly dry, try adding a tablespoon of water to continue caramelizing. The water should sizzle and quickly evaporate so do not add too much water.
When the onions are caramelized, remove from skillet and place in a bowl. Add the remaining 1 teaspoon of oil to the skillet along with mushrooms and 1/2 teaspoon of salt. Cook mushrooms until softened, about 5 minutes. Remove from skillet; keeping the liquid that has accumulated in the skillet.
Preheat broiler in oven.
Spread bread slices with butter and place onto cooking sheet. Cook under broiler for 1 minute. Remove from oven.
Place caramelized onions on each of 4 slices of bread then the mushrooms and shredded cheese. Top with second slice of bread gently press down onto each sandwich and toss baking sheet back into oven. Heat under broiler until cheese has melted; 1-2 minutes.
Remove from oven and allow to slightly cool. Serve with sliced pepper, carrots and orange wedges.