Step 1

Adjust oven racks to lowest and middle positions and heat oven to 500 degrees. Drain tomatoes in fine-mesh strainer set over bowl, pressing with rubber spatula to extract as much juice as possible. Combine 1¾ cups drained tomato juice, sugar, and lime juice in bowl and set aside; discard extra drained juice.

Step 2

Combine tomatoes, onion, chiles, oil, chili powder, garlic, and ½ teaspoon salt in bowl, then spread mixture out evenly on rimmed baking sheet. Wrap tortillas in aluminum foil and place on lower rack. Place sheet with tomato mixture on upper rack and roast until charred in spots, 35 to 40 minutes, stirring and redistributing into even layer halfway through roasting.

Step 3

Remove sheet from oven and place inside second rimmed baking sheet. Carefully stir reserved tomato juice mixture into roasted vegetables, season with salt and pepper to taste, and spread into even layer. Sprinkle cheese over top and, using back of spoon, hollow out eight 3-inch-wide holes in mixture. Crack 1 egg into each hole and season with salt and pepper.

Step 4

Bake until whites are just beginning to set but still have some movement when sheet is shaken, 7 to 8 minutes for slightly runny yolks or 9 to 10 minutes for soft-cooked yolks, rotating sheet halfway through baking.

Step 5

Remove sheet from oven and top with avocado, scallions, and cilantro. To serve, slide spatula underneath eggs and sauce and gently transfer to warm tortillas.