Heat the oil in a medium skillet over high heat. Add the bell pepper, mushroom, onion, and garlic and season with salt and pepper. Cook the vegetables, stirring occasionally, until lightly browned and soft, about 6 minutes. Transfer the mixture to a bowl. Add the ham to the skillet and cook, turning once, until lightly browned, about 1 minute.
Layer the vegetable mixture, ham, and cheese between the two slices of bread. Put the sandwich in the grill and grill until hot and crispy, about 4 minutes. (Alternately, grill on a cast iron grill pan, weighed-down with a foil-wrapped brick or other heavy item.)
Cut the sandwich in 1/2 and serve immediately.
This recipe was provided by a chef, restaurant or culinary professional. It has not been tested for home use.