Ham and Cheese Breakfast Casserole

Name: Ham and Cheese Breakfast Casserole
Ingredients: 6 tablespoons butter, plus more for greasing dish; 1 large onion, thinly sliced; Kosher salt and freshly ground black pepper; 4 cups 1/2-inch bread cubes (crusts removed); 8 ounces cremini mushrooms, sliced; 8 large eggs; 1 1/4 cups half-and-half; 1 teaspoon Dijon mustard; Pinch cayenne; 4 ounces ham, diced; 1 1/2 cups shredded Gruyere, Emmental or Jarlsberg (about 4 ounces); 2 small plum tomatoes, sliced very thinly; 2 tablespoons grated Parmesan; 2 tablespoons chopped parsley, for garnish