Pour three tablespoons olive oil into a 12-inch non stick, ovenproof skillet over medium-high heat. Cut the chorizo into slices and add to the pan; fry for 5 minutes. Chop the onion and add to the skillet along with the Alexia Hashed Browns. Fry until the onions start to soften, about 5 minutes. Reduce the heat and cover the skillet. Cook until the potatoes are tender, about 8 minutes.
Remove the cover, raise the heat back to medium-high, and cook until the potatoes are brown and crispy, about another 4 minutes. Meanwhile, break the eggs into a large bowl and add the milk. Season the egg mixture with salt and pepper, then whisk until frothy. Pour the egg mixture into the pan, shaking the pan to distribute the eggs evenly. Put the pan into the oven and cook until puffy and set, about 12 to 15 minutes.
Turn out onto a cutting board and let it cool to room temperature. Toss the baby greens with the remaining oil and lemon juice; season with salt and pepper. Place the greens on top of the frittata, cut it into thin wedges and serve.