Heat the olive oil in a 10-inch cast iron skillet over medium heat.
Add the chorizo and break it into small crumbles with a spatula. Cook for 5 to 6 minutes, stirring often, until browned and no pink remains, reaching an internal temp of 160 F / 71 C.
Add the onion and bell pepper. Cook for 4 to 5 minutes, stirring occasionally, until softened.
Stir in the cumin and smoked paprika, then add the spinach. Cook for 1 minute, just until the spinach wilts.
Push the mixture toward the edges of the skillet and make 6 small wells. Crack an egg into each well.
Season the eggs with salt and pepper. Cover the skillet and cook for 4 to 5 minutes over medium heat, until the whites are fully set and opaque but the yolks are still soft.
Sprinkle the shredded cheddar over the top. Cover for 1 more minute, just until the cheese melts.
Remove the skillet from the heat. Top with sliced avocado and chopped cilantro.
Serve straight from the skillet with lime wedges on the side.