Preheat the oven to 375 degrees . In a medium ovenproof skillet, heat 1 tablespoon olive oil over medium heat. Add the chorizo and cook, stirring, until browned, 6 to 8 minutes. Using a slotted spoon, transfer the chorizo to a bowl. Add the onion to the skillet, season with salt and pepper and cook until softened, 6 to 8 minutes. Stir in the bell pepper and cook until crisp-tender, 3 to 4 minutes; add the onion and bell pepper to the chorizo. Add 2 tablespoons olive oil to the skillet. Add the potato, season with salt and pepper and cook, stirring occasionally, until golden, about 8 minutes. Stir in the chorizo mixture, eggs and two-thirds of the mozzarella; season with salt and pepper. Cook, undisturbed, until the bottom sets, about 2 minutes. Transfer the skillet to the oven and bake until the center is just set, 6 to 8 minutes.
Preheat the broiler. Sprinkle the remaining mozzarella on top of the frittata and broil until the cheese is golden, about 2 minutes. Let rest for 5 minutes before slicing.
Meanwhile, in a large bowl, whisk together the vinegar and remaining 1 tablespoon olive oil. Add the greens and toss; season with salt and pepper. Serve with the frittata.