Preheat oven to 400F.
Heat a 12-inch, nonstick, oven-safe skillet over medium-high heat. Add EVOO and chorizo, and cook until the chorizo is crispy, about 3 minutes.
Add the sliced potatoes and onions, and continue to cook, stirring frequently for about 5 minutes or until the potatoes are tender. Add the garlic and continue to cook for 1 minute.
Beat eggs together with half-and-half. Whisk in the salt and pepper. Pour the eggs over the filling. Let the eggs set. Using a spatula, raise eggs off the bottom of the skillet, allowing more of the liquid egg to settle. When the frittata has set, sprinkle with the cheese and transfer to the oven. Cook for 10-12 minutes until top is deep golden brown. Remove let stand 5 minutes. Garnish with parsley, cut into wedges and serve.