Preheat the oven and a pizza stone at 500˚ F for at least 30 minutes. Roll out the pizza dough into a 12-14 inch round. Lightly brush the surface of the dough with olive oil.
Cut the tough woody stems off the ends of the asparagus spears. Use a vegetable peeler to shave the spears into ribbons. You likely will not need all of the asparagus, but use more ribbons than you think you need because it will cook down in the oven.
Place the sliced mozzarella over the pizza dough in an even layer. Pile the asparagus shavings over the top of the mozzarella. Dot the surface of the pizza with the garlic herb cheese. Season with kosher salt and pepper.
Transfer the pizza to the preheated pizza stone and bake until the cheese is melted and bubbling and the crust is lightly browned, about 12 minutes. Remove from the oven and let cool slightly before slicing and serving.