1. Preheat the oven to 500°. Preheat a pizza stone or generously oil a large baking sheet. Heat 1 tablespoon of the olive oil in a large skillet. Add the asparagus and cook over high heat, stirring occasionally, until lightly browned, about 5 minutes; transfer to a bowl. Add the ham and scallions to the asparagus and season with salt and pepper. Let cool slightly. Add half of the shredded cheese.
2. On a lightly floured surface, roll or stretch the dough to a rough 14-inch round. Transfer the dough to a floured pizza peel or rimless cookie sheet, or to the oiled baking sheet. Top the pizza with the asparagus mixture, leaving a 1-inch border of dough. Brush the border with the remaining 1 teaspoon of olive oil. Scatter the grated cheese and the remaining shredded cheese over the top.
3. Slide the pizza onto the hot stone, if using, and bake for about 10 minutes on the stone or 16 minutes on the baking sheet, until the crust is golden and the cheese is bubbling. Transfer the pizza to a rack and let cool slightly before serving.
Wine Recommendation: A clean, light white, such as the 1997 Torres Viña Sol from Spain or the 1997 Domaine de la Jalousie Sauvignon from France, is a refreshing choice.