In food processor or blender, place chipotle chiles. Cover; process until smooth. Measure 4 teaspoons puree (refrigerate remaining puree for later use, if desired).
In large bowl, mix beef, 4 teaspoons puree and steak seasoning just until combined. Shape mixture into 8 (4-inch) patties; place 1 cheese slice on each of 4 patties. Top with remaining 4 patties, pressing edges to seal. Cover; refrigerate at least 30 minutes.
Heat gas or charcoal grill. Place patties on grill over medium-high heat. Close grill; cook 14 to 16 minutes, turning once, until meat thermometer inserted in center of patties reads 160°F. Place buns, cut sides down, on grill for last 1 to 2 minutes of cooking time or until toasted. Serve burgers on buns with desired toppings.