4 portobello mushrooms, stems trimmed and discarded
Garlic Oil (recipe below)
Salt
Freshly ground pepper
8 (8-inch) flour tortillas
1 cup shredded Fontina cheese
2 teaspoons chopped fresh rosemary or a combination of rosemary, sage and thyme
Recipe
Fontina is a mild, soft Italian cheese;
it is more flavorful than Monterey Jack or mozzarella, but either of those may be substituted. Garlic oil is great for grilling vegetables, meats and poultry when you want just a bit more flavor. It's also good in a vinaigrette. Make it in small batches because it tends to spoil quickly, even when refrigerated. If time is short, plain extra virgin olive oil may be substituted here for the garlic oil.
1. Build a charcoal fire in an outdoor grill and let it burn until the coals are covered with white ash. In a gas grill, preheat on high.
2. Lightly oil the cooking rack (grate). Brush the mushroom caps liberally with garlic oil and lightly season them with salt and pepper. Place the mushrooms on the grill and cover. Grill, turning once, until the mushrooms are tender, about 6 minutes. Transfer them to a cutting board and slice into 1/2-inch-wide strips.
3. Place 4 tortillas on a work surface and sprinkle each with 1/4 cup of the cheese. Top with equal amounts of the mushroom strips, sprinkle with the herbs, then carefully place each on the grill. Top each with one of the remaining tortillas. Grill the quesadillas until the underside is lightly browned, about 45 seconds, then turn (carefully) and grill to brown the other side. Cut each quesadilla into 6 wedges and serve immediately.