Bring a large pot of water to a boil over medium heat. Add the potato slices and cook until they are just tender. Drain and reserve.
Meanwhile, in a medium nonstick saute pan, heat the olive oil and add the onions. Season with salt and black pepper, to taste, and cook the onions until they are soft and starting to caramelize, about 5 minutes. Drop in the sliced chorizo and the garlic and cook until the sausage starts to brown. Remove the pan from heat.
In a large bowl, beat the eggs until they are light yellow in color. Stir in the milk, green onions, and Cheddar and combine until incorporated. Adjust the seasonings with salt and black pepper. Add the chorizo mixture and potatoes to the bowl and stir gently. Return the entire mixture back to the saute pan. Put the pan in the oven and bake until the eggs set, about 15 minutes. Remove from the oven and let the tortilla rest in the pan 10 minutes before inverting it. Using a large clean plate as an aid, flip the tortilla over and slide it out onto a large cutting board. Slice the tortilla into wedges and arrange on serving dishes. Serve it warm or at room temperature.
If serving this as an appetizer, chill it before slicing into tiny wedges, then reheat the wedges on a baking sheet in the oven. You'll get a cleaner cut that way.