Mix the oil, ¼ teaspoon salt, and oregano in a medium-sized bowl. Add the diced potatoes and stir to coat them evenly in the oil. Spread them in an even layer on a baking dish. Roast them for 20 minutes or until fork tender.
Brown the chorizo in an oven-safe, 12" non-stick pan over medium-high heat. Break it up as it cooks so there are no large chunks. Once it’s cooked, after about 10 minutes, turn the heat off and drain off the excess fat.
When the potatoes are done, lower the oven to 350°F. Add the potatoes and cilantro to the pan with the chorizo. Stir so the chorizo is evenly distributed among the potatoes. Sprinkle half of the cheese over the top.
Whisk the eggs, milk, and 1/4 teaspoon of salt in a small bowl. Pour the eggs over the potatoes and chorizo. Sprinkle the rest of the cheese over the top.
Bake the frittata for 10 to 15 minutes or until it is set in the center. Let the frittata rest for a few minutes before slicing and serving it.
Notes
You can make parts of the frittata ahead. Roast the potatoes and cook the chorizo ahead and store them in the refrigerator until you're ready to bake the frittata. It may need a little longer bake time if you do this since the ingredients and pan will be cold going into the oven.If you use a different sized pan, you will need to adjust the baking time. A 10" pan will give you a thicker frittata, but it will take longer to bake.Leftovers will keep in the refrigerator for a few days. I like to reheat them in the microwave at 50% power. This warms the egg gently so it doesn't turn rubbery. That said, the leftovers are delicious cold, too.