Instructions

Adjust oven rack to middle position and heat oven to 500 degrees. Line rimmed baking sheet with aluminum foil. Toss 1½ pounds halved cherry tomatoes, 1½ cups fresh or thawed frozen corn, 1 halved and thinly sliced onion, 2 tablespoons vegetable oil, 3 minced garlic cloves, 2 teaspoons minced canned chipotle chile in adobo sauce, 2 teaspoons minced fresh oregano, 1 teaspoon ground cumin, ½ teaspoon ground coriander, ½ teaspoon table salt, and ¼ teaspoon pepper together, then spread onto prepared sheet. Roast tomato mixture, stirring occasionally, until tomatoes are softened and skins begin to shrivel, 10 to 15 minutes. Remove from oven.
Meanwhile, using fork, poke center of 8 corn tortillas 3 or 4 times (to prevent puffing and allow for even cooking). Heat ¾ cup oil in 8-inch skillet over medium heat to 350 degrees. Line second rimmed baking sheet with several layers of paper towels.
Working with 1 tortilla at a time, add to hot oil and place metal potato masher on top to keep tortilla flat and submerged in oil. Fry until crisp and lightly browned, 45 to 60 seconds (no flipping is necessary). Transfer fried tortilla to paper towel–lined sheet. Repeat with remaining tortillas.
Using spoon, make 8 indentations, 2 to 3 inches wide, in tomato mixture in sheet. Working with 8 eggs, crack 1 egg into each indentation. Bake until egg whites are just set and yolks are still runny, 5 to 7 minutes, rotating sheet halfway through baking.
Spread 2 tablespoons warm refried beans over each tostada, then top with tomato mixture and eggs. Sprinkle with 2 ounces queso fresco and 3 tablespoons chopped cilantro and serve immediately.