Beat eggs with milk, salt and pepper in a small bowl. Turn on broiler and position a rack at the top. Heat oil in a medium, oven-proof, non-stick skillet over medium heat. Add potatoes and cook until browned, stirring frequently. Reduce heat to low. Add garlic and chorizo to skillet and cook 1 minute longer. Add eggs and cook folding up edges of tortilla to allow uncooked egg to run underneath, about 3 minutes. Sprinkle cheese over tortilla and place under broiler until eggs as just done and cheese melts. Garnish with chopped basil. * Don't substitute Mexican chorizo, it's a completely different sausage. You can probably find it at Whole Foods or a similar store, but if you can't find Spanish chorizo just skip it. ** Manchego is a Spanish sheep's milk cheese. Again, you can probably find it at Whole Foods or a specialty cheese shop. Gruyere makes a decent substitute.