With the rack in the middle position, preheat the oven to 350°F (180°C).
Remove the papery husks from the tomatillos. Wash the tomatillos well under warm water to remove any sticky residue. Cut into quarters.
On a non-stick or foil-lined baking sheet, combine the tomatillos, onion, jalapeño and garlic with the oil. Season with salt and pepper. Cook for 10 minutes. Stir the vegetables. Set the oven to broil. Continue cooking for 15 minutes or until the onions are tender and the tomatillos are slightly charred. Let cool.
In a food processor, coarsely chop the cilantro and charred vegetables. Use a spatula to scrape down the sides of the food processor as needed. Adjust the seasoning.
Serve warm or cold. A great topping for nachos, tacos or white fish. The salsa will keep in an airtight container for 1 week in the refrigerator.