Prepare grill for direct-heat cooking over hot charcoal (high heat for gas); see Grilling Procedure . Put parmesan in a medium bowl and add olive oil in a slow stream, whisking. Whisk in lime juice, garlic, chipotles, and 1/4 teaspoon each of salt and pepper. Rub vegetable oil on corn and cut sides of avocados, then season with 1/8 teaspoon each of salt and pepper. Grill avocados, cut sides down, and corn, covered only if using a gas grill, turning corn occasionally, until golden-brown, 3 to 4 minutes. Peel avocados and thinly slice. Cut corn kernels from cobs. Toss romaine with dressing and serve topped with avocado and corn.