1. Combine rice with 3 cups water, cover and bring to a boil. Reduce to a low simmer and cook 40 minutes. Remove from heat and let stand 10 minutes. Fluff with a fork and transfer to a large bowl.
2. Meanwhile, heat grill or grill pan to medium-high. Toss shrimp with 1 tbsp of the oil, 1/4 tsp of the salt and 1/8 tsp of the cayenne.
3. Thread shrimp onto skewers. Grill corn 3 to 5 minutes per side, turning 3 times (12 to 20 minutes total). Grill red onion 3 minutes per side, and avocado and shrimp 2 minutes per side.
4. Cut kernels from corn cobs, dice onion and avocado, and remove shrimp from skewers. Toss in bowl with cooked rice. Gently toss with lime juice and remaining 1 tbsp oil, 3/4 tsp salt and 1/8 tsp cayenne. Garnish each serving with 1 tbsp cheese.