Preheat and prep: Heat the oven to 375°F (190°C).
Grease a 9x13-inch baking dish with nonstick spray or butter.
Brown the chorizo: In a large skillet over medium heat, cook the chorizo, breaking it up, until browned and cooked through, about 6–8 minutes. Transfer to a plate, leaving a little fat in the pan.
Sauté the veggies: Add olive oil if needed. Cook onion, bell peppers, and poblano with a pinch of salt until softened and lightly browned, about 6–8 minutes.
Stir in jalapeños and garlic, cook 1 minute more.
Season the base: Sprinkle chili powder, cumin, smoked paprika, and oregano over the veggies. Cook 30 seconds to bloom the spices. Return chorizo to the skillet and stir in the green chiles.
Taste and season with salt and pepper.
Layer the potatoes: Spread thawed hash browns (or par-cooked diced potatoes) in the baking dish. Season lightly with salt and pepper. Drizzle with 1 tablespoon olive oil if using fresh potatoes.
Add the chorizo mixture: Spoon the chorizo-veg mixture evenly over the potatoes.
Cheese layer: Sprinkle 1 1/2 cups of the shredded cheese over the top.
Whisk eggs: In a large bowl, whisk eggs, milk, 1/2 teaspoon salt, and 1/4 teaspoon black pepper until smooth.
Stir in chopped cilantro.
Pour and settle: Pour the egg mixture evenly over the casserole. Gently shake the pan so eggs seep through the layers.
Bake: Cover loosely with foil and bake for 25 minutes. Remove foil, sprinkle remaining 1/2 cup cheese on top, and bake another 15–20 minutes until the center is set and the edges are golden.
Rest and garnish: Let it rest 10 minutes to firm up.
Top with more cilantro and serve with salsa, hot sauce, avocado, and lime.