A drizzle of truffle oil just before serving elevates this pizza's ingredients -- asparagus, leeks, shiitake mushrooms, and Taleggio cheese -- even further.
Heat olive oil in a large skillet over medium heat until hot but not smoking. Add leeks; cook, stirring, until beginning to soften, about 5 minutes. Add mushrooms; cook until tender and juices have evaporated, about 4 minutes. Add the asparagus and wine; cook until asparagus is bright green and wine has evaporated, about 2 minutes. Stir in thyme; season with salt and pepper. Set aside.
Heat a grill until medium-hot. Generously brush one side of pizza dough with olive oil; grill, oiled side down, until underside is golden brown and top begins to bubble, 3 to 5 minutes. Quickly brush top with olive oil; flip crust. Top with a thin layer of cheese and some of the asparagus mixture. Grill until cheese is just melted, topping is hot, and crust is cooked through, 3 to 5 minutes more.
Slide 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.