Beef Burgers

Fit a food grinder with a grinding plate with about 1/4-inch holes. Combine chuck and sirloin in a bowl, and slowly grind meat into another bowl. Mix gently, and shape into six 1-inch-thick patties. Cover, and refrigerate until cold and firm, about 30 minutes.

Preheat grill to medium-high. (If you are using a charcoal grill, coals are ready when you can hold your hand 5 inches above grill for 3 to 4 seconds.) Brush grill with oil. Generously season both sides of patties with salt and pepper. Grill, flipping once, until burgers are cooked through, about 5 minutes per side. Top each burger with a cheese slice during the final 30 seconds of cooking. Grill buns, cut sides down, until lightly toasted, about 30 seconds.

Lightly drizzle onion with oil, and toss to coat. Season with salt and pepper. Grill, turning once, until tender, about 2 minutes.

Combine mustards in a small bowl. Spread mustard mixture on cut sides of bun halves. Divide lettuce, burgers, tomato, and onion among bottom halves. Sandwich with top halves.