The gooey filling for these juicy burgers was inspired by the Mexican dip chile con queso, made with melted cheese and roasted chiles. All-Time Favorite Burgers
Light a grill. Rub the chiles with olive oil. Thread the jalapeños and garlic onto a skewer and grill until charred all over. Using tongs, repeat with the Anaheims. Peel the chiles and discard the stems and seeds. Peel the garlic. Chop the chiles and garlic and transfer to a bowl. Fold in the cheese and season with salt and pepper.
Cut eight 6-inch squares of wax paper; divide the beef among them. Pat each portion into a 5-inch round, a little thicker in the center. Using a 1/4 cup measure, mound one-fourth of the cheese mixture in the centers of 4 patties. Top with the remaining patties; press the edges to seal. Flatten the centers so that the burgers are even. Brush with oil and season with salt and pepper. Brush the cut sides of the rolls with oil.
Lightly oil the grate. Grill the burgers over a hot fire, turning once, about 7 minutes for medium to medium-rare meat. Toast the kaiser rolls. Place the burgers on the rolls and top with lettuce leaves, onion and tomato. Serve with mayonnaise and ketchup.