Meanwhile, toss the asparagus with 1 tablespoon oil and sprinkle with salt and pepper. Brush the remaining tablespoon oil all over the crust.
Grill the asparagus, turning, until charred and almost tender, about 6 minutes. Place the crust on the grill next to the asparagus. When the bottom browns, flip the crust over and sprinkle half of the cheese on top. Arrange the tomatoes over the cheese in a single layer and sprinkle the remaining cheese on top.
As soon as the cheese melts, transfer the asparagus to the pizza in a single layer. Remove from the heat and sprinkle the basil on top. Cut into 8 wedges.