1. Make the sauce. In a small non-stick skillet over medium-high heat, roast the tomatillos (start them cut-side down) and garlic until soft and browned, 3 or 4 minutes per side. (If a non-stick skillet is unavailable, line a regular skillet with aluminum foil.) Scoop the tomatillos and garlic into a blender or food processor, add the chile and 1/2 cup water and blend until smooth. Taste and season with salt, usually a generous ½ teaspoon.
2. Finish the dish. Film a heavy-bottomed skillet with vegetable oil and bring to medium heat. Add the slices of cheese and sear until golden brown, about 2 to 3 minutes per side. Pour in the salsa and bring to a rolling boil. Scoop the sliced onion into a strainer and rinse under cold water. Sprinkle over the dish, along with the chopped cilantro, and serve with warm tortillas.