Grilled pizzas with leeks, asparagus, and mushrooms

2 tablespoons extra-virgin olive oil, plus more for brushing
2 medium leeks, halved lengthwise, cut into thin half-moons, and rinsed well
8 ounces shiitake mushrooms, stemmed and cut into 1/ 4 -inch-thick slices
8 ounces thin asparagus, trimmed and cut into 1 1/ 2 -inch pieces
1/ 4 cup dry white wine
1 tablespoon finely chopped fresh thyme, plus more for garnish
Coarse salt and freshly ground pepper
Pizza Dough
4 ounces Taleggio or other soft cheese (such as Camembert or Brie), sliced Truffle oil, for drizzling (optional)

Heat the olive oil in a large skillet over medium heat until hot but not smoking. Add the leeks; cook, stirring, until beginning to soften, about 5 minutes. Add the mushrooms; cook until tender and juices have evaporated, about 4 minutes. Add the asparagus and wine; cook until the asparagus is bright green and the wine has evaporated, about 2 minutes. Stir in the thyme; season with salt and pepper. Set aside.
Heat a grill until medium-hot. Generously brush one side of the pizza dough with olive oil; grill, oiled side down, until the underside is golden brown and the top begins to bubble, 3 to 5 minutes. Quickly brush the top with olive oil; flip the crust. Top with a thin layer of cheese and some of the asparagus mixture. Grill until the cheese is just melted, the topping is hot, and the crust is cooked through, 3 to 5 minutes more.
Slide the pizza with a large spatula onto a cutting board. Season with salt and pepper. Sprinkle with more thyme and with a small amount of truffle oil, if desired. Repeat to make more pizzas.
MAKES SIX 9 - INCH PIZZAS