Preheat the oven to 400°F. Toss the sweet potatoes with 2 tablespoons of olive oil and arrange in an even layer on a large rimmed baking sheet. Season with salt and pepper. Roast for 40 to 45 minutes, until tender and golden brown.
Meanwhile, heat the remaining tablespoon of olive oil in a large skillet over medium-high heat. Add the chorizo and cook for 8 to 10 minutes, breaking up the meat with a spoon, until cooked through. Add the poblano chiles, bell peppers, and shallots, season with salt and pepper, and cook for 4 to 5 minutes, until the vegetables are tender. Stir in the spinach, cilantro, and butter and cook for 1 to 2 minutes, until the spinach is wilted. Stir in the sweet potatoes.
To serve, transfer the hash to plates. Place one fried egg over each plate and top with the cheese and avocado slices.