Preheat grill to medium (350°F to 400°F). Brush avocado halves evenly with 1 tablespoon each of the oil and lime juice. Sprinkle evenly with 1 teaspoon of the salt and 1/4 teaspoon of the pepper. Grill, cut side down, uncovered, until edges begin to char, 5 to 7 minutes. Carefully remove from grill; set aside.
Toss together tomatoes, cilantro, and remaining 2 tablespoons each oil and lime juice, 1/2 teaspoon salt, and 1/4 teaspoon pepper in a medium bowl. Let stand 5 minutes.
Place avocado halves, cut side up, on a platter. Top evenly with tomato mixture, Cotija, and Pickled Red Onions.
