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.
Corn and avocados can be grilled, in batches if necessary, in a lightly oiled hot grill pan over medium-high heat.
