Brown ground chuck in medium frying pan with mushrooms, onion and garlic. Drain excess fat; remove beef mixture from pan and wipe pan clean.
Melt 1 teaspoon butter over medium-high heat in the same pan. Brown two slices of bread. Flip bread over and top each with one slice Swiss cheese. Top one slice of bread with 1/3 to 1/2 cup hamburger mixture. Place second slice of toasted bread on top and flip sandwich over one more time to melt cheese.
Keep prepared Toasty Grilled Beef and Cheese sandwiches warm in oven while cooking the others.