Step 1
Preheat oven to 400°. Place 1 small yellow onion, very coarsely chopped, 3 garlic cloves, 1 serrano chile, halved, and 8 oz. tomatillos (about 4 medium), husks removed, rinsed, in a medium bowl. Drizzle with vegetable oil, season with kosher salt, and toss to coat. Arrange tomatillos on a rimmed baking sheet; roast 10 minutes. Add onion, garlic, and chile; roast until charred in spots, 20–25 minutes. Let cool slightly.
Step 2
Blend 1 small bunch cilantro, coarsely chopped, and ½ cup water in a blender until smooth. Add roasted vegetables, 2 Tbsp. fresh lime juice, and 1 tsp. Diamond Crystal or ½ tsp. Morton kosher salt. Blend until mostly smooth. Set salsa aside.
Step 3
Beat 8 large eggs in a medium bowl with a fork to combine; season with salt.
Step 4
Heat remaining 6 Tbsp. vegetable oil in a large nonstick pan over medium-high. Drop in a ½”-thick corn tortilla strip; if oil sizzles it is ready (heat a little longer if needed). Working in 2 batches, cook 4 corn tortillas, halved, cut into ½”-thick strips, stirring often to avoid clumps and adjusting heat as needed, until golden, 2–3 minutes per batch. Using tongs or a slotted spoon, transfer to paper towels; season with salt.
Step 5
Pour off all but 1 Tbsp. oil from pan. Add 3 Tbsp. unsalted butter and heat over medium until melted. Add 1 medium white onion, chopped; season with salt. Cook, stirring occasionally with a heatproof rubber spatula, until slightly softened and translucent, about 5 minutes.
Step 6
Pour eggs into pan and cook, stirring gently and adjusting heat to medium-low if you prefer a softer scramble, just until eggs start to come together, about 45 seconds. Add fried tortillas and quickly stir into eggs. Immediately add 3 oz. sharp cheddar, coarsely grated, and cook, stirring occasionally, until cheese is melted, about 1 minute. Transfer to a plate and season with freshly ground pepper.
Step 7
Serve migas with flour tortillas, sliced avocado, pickled sliced jalapeños, lime wedges, and reserved salsa alongside.
