1. Preheat broiler to high; place a rack about 8 inches from heat source. Combine avocado, shallot, lime juice, crushed red pepper and 1/2 tsp. salt in a bowl. Lightly mash avocado with back of a fork to break up chunks. Cover with plastic wrap, pressing directly onto surface of guacamole, and chill until ready to serve.
2. Sprinkle beef with chili powder and 1 tsp. salt. Mix gently with your hands to distribute seasonings. Shape into 4 patties. Broil hamburgers until they reach desired doneness, turning once, about 8 minutes for medium-rare. Serve hamburgers on buns with guacamole on top.