3 ounces thinly sliced prosciutto
2 tablespoons extra-virgin olive oil, plus more as needed
8 ounces assorted sliced mushrooms
2 teaspoons minced fresh rosemary
1 teaspoon minced garlic, plus 1 clove cut in half
1/3 cup dry red wine
Freshly ground black pepper
Twelve 4-inch-wide slices rustic bread
½ teaspoon good-quality truffle oil, or as needed (optional)
Six 6-ounce burger patties (80-20 ground beef or ground chuck)
6 ounces Taleggio cheese, coarsely grated (may substitute fontina; semi-soft cheeses like Taleggio are easier to grate when you put them in the freezer for 30 minutes beforehand)
Preheat the oven to 350 degrees. Line a rimmed baking sheet with parchment paper. Lay the prosciutto on it in a single layer; bake (middle rack) for 12 minutes. Cool completely, during which time the prosciutto will crisp up.
Prepare the grill for direct heat. If using a gas grill, preheat to medium-high (about 450 degrees). If using a charcoal grill, use a metal chimney to prepare your briquettes; once the charcoal is gray and glowing red, distribute the briquettes evenly under the cooking area. The grill should be ready when you can place your hand about 6 inches over the grate for 3 to 4 seconds without pulling it away.
Heat the 2 tablespoons of extra-virgin olive oil in a large skillet over medium-high heat. Once the oil shimmers, add the mushrooms, rosemary and a pinch of salt; reduce the heat to medium and cook for about 6 minutes, stirring occasionally until the mushrooms have started to turn golden. Add the minced garlic and cook, stirring, for 1 minute. Pour in the wine; cook until it has evaporated, then season lightly with pepper and remove from the heat.
Brush both sides of the bread slices lightly with extra-virgin olive oil. Place on the grate and grill (uncovered) for 1 to 2 minutes per side, until they are nicely marked. Rub one side of each grilled slice with one of the cut sides of the garlic clove. Place 2 grilled slices of bread on each plate.
Stir the truffle oil, if using, into the cooled mushrooms.
Brush the burger patties lightly with extra-virgin olive oil and season both sides lightly with salt and pepper. Place the burgers on the grate; grill (uncovered) for 3 minutes. Turn the burgers over; close the lid and grill them for 2 minutes.
Working quickly, top each burger with the crispy prosciutto, one-sixth each of the mushroom mixture, and, last, the cheese. Close the lid and cook until the cheese has melted, 1 to 2 minutes.
Sandwich the burgers between the grilled bread and serve. There go delightfully with grilled corn and/or a tomato and cucumber salad.
Note: The USDA recommends cooking ground meat to well done. These burgers will be medium to medium-rare, which is how I like them. If you do, too, buy the meat from a reliable source. Or grind it yourself. If you don't own a grinder, cut shoulder or chuck meat into 1-inch cubes and freeze it for 30 minutes. Pulse it, in thirds, in a food processor until ground to 1/8- to ¼-inch pieces.