1. Place the tomatillo quarters in a medium saucepan. Add enough water to cover halfway. Cover and cook over medium heat until very soft, about 10 minutes. Strain, reserving ½-cup of the cooking water.
2. Set a cast-iron skillet over high heat. Add the garlic and roast, turning until the peel has blackened on all sides, about 10 minutes. Meanwhile, in the same skillet, blacken the chili, about 2 minutes per side.
3. Rinse the chili briefly in cold water and break half of it into small pieces over a blender, removing the seeds and veins. (For intense heat, add the full chili, but start with half and add more to taste.) Peel the garlic and add it to the blender along with the reserved cooking liquid and a pinch of salt. Blend until smooth. Add the cooked tomatillos and pulse briefly. The sauce should have a medium consistency. If too thick, add more water; if thin, it will thicken as it sits. Makes about 1 cup. Adapted from ‘‘The Art of Mexican Cooking,’’ by Diana Kennedy.