Place rack in the top third of the oven and preheat the oven to 450 degrees F. Generously dust a large baking sheet with cornmeal or flour or line with parchment paper.
Prepare the asparagus: Lay each asparagus spear on the counter and hold by the “tough” end. With a vegetable peeler, shave long ribbons of asparagus by sliding the peeler from the base to the top of the stalk. Repeat with remaining stalks. (The pieces may be different sizes and some may be too small to shave.) Discard tough stem ends. In a small bowl, toss the shavings with 2 teaspoons olive oil and 1/2 teaspoon salt. Set aside.
In a large skillet over medium heat, heat 2 tablespoons olive oil. Add leeks, 1/4 teaspoon salt, and 1/4 teaspoon pepper. Cook leeks until softened, about 8 minutes, then transfer to a plate. Add the remaining 2 tablespoons of olive oil to the skillet. Add the turkey, remaining 1/2 teaspoon salt, 1/4 teaspoon pepper, red pepper flakes, and fennel. Sauté until the meat is fully cooked and no pink remains; about 4 minutes.
On a lightly floured surface, shape dough into an 11x14-inch rectangle, then transfer to the prepared baking sheet.
Brush dough liberally with olive oil, then top with the leeks, turkey, and pecorino. Pile the asparagus on top. (It may seem like a lot of asparagus, but it will cook down as it bakes.)
Carefully side the pizza onto the prepared peel/pan and bake for about 15 minutes, until bubbling and crisp. Drizzle with oil and serve.
TO STORE: Leftover pizza may be stored for up to 2 days in the fridge.
TO REHEAT: Enjoy cold or warm in the oven or microwave until heated through.