Place a 12-inch frying pan over medium-high heat. When hot, add ears or corn and toast until browned, turning as needed (approximately 10 minutes). Remove from pan and let cool. If using frozen corn, follow same directions.
In 4-quart pan, combine broth, carrot, onion and garlic. Bring to boil, then simmer until veggies are tender (approximately 10 minutes).
While broth simmers, cut kernels off corn cobs using a sharp knife. Add to soup mixture. Cover and simmer for 5 minutes.
Puree soup in blender until smooth (do in batches), then rub through a fine sieve over bowl. Discard solids.
Serve soup hot or cold, topped with basil salsa and/or basil sprigs.