Step 1

Preheat broiler with oven rack in middle of oven. Place tomatoes, cut sides up, and onion on a rimmed baking sheet, and broil in preheated oven on middle rack until charred, 16 to 22 minutes. Let cool 15 minutes, and set aside.

Step 2

Meanwhile, heat a large cast-iron skillet over medium. Add chiles and garlic cloves, and cook, turning often, until chiles are fragrant, about 4 minutes. Remove chiles from skillet. Continue cooking garlic cloves, turning occasionally, until blackened in spots and softened, about 10 minutes total. Let garlic cloves cool 10 minutes; peel and set aside.

Step 3

Bring 1 quart water to a boil in a small saucepan over medium-high. Add toasted chiles, and boil, stirring occasionally, until chiles are softened, about 10 minutes. Drain, reserving 1 1/2 cups cooking liquid.

Step 4

Combine tomatoes, onion, garlic, chiles, oregano, salt, reserved cooking liquid, and 1 cup cilantro stems in a blender. (Reserve any remaining cilantro stems for another use.) Process until smooth, about 20 seconds. Pour mixture through a fine wire-mesh strainer into a bowl; discard solids. Set red chile sauce aside.

Step 5

Heat oil in a large (12-inch) nonstick skillet over medium. Crack eggs into skillet, leaving 1 inch between them. Cook until edges are set and starting to brown, about 2 minutes. Cover skillet, and cook until whites are set and yolks reach desired degree of doneness, 2 to 3 minutes for runny yolks. Transfer eggs to a plate; tent with aluminum foil to keep warm. Add red chile sauce to skillet over medium. Bring to a simmer. Pour red chile sauce over chips in a large bowl; toss to coat. Divide chip mixture evenly among 4 plates. Top evenly with eggs, avocado slices, queso fresco, crema, and desired amount of cilantro leaves. Serve immediately.