Remove white papery skin from garlic head (do not peel or separate the cloves). Coat garlic with cooking spray. Wrap garlic head in foil. Bake at 400° for 45 minutes or until tender; cool 10 minutes. Separate cloves; squeeze to extract garlic pulp. Discard skins. Combine garlic pulp and olive oil in a small bowl, stirring until smooth.
Preheat oven to 500°.
Place a pizza stone on bottom oven rack. Preheat pizza stone 30 minutes.
Combine onion, vinegar, and 2 teaspoons salt in a bowl; let stand 20 minutes. Remove 1 cup onion mixture with a slotted spoon; set aside. Reserve remaining onion mixture for another use.
Cook asparagus in boiling water 2 minutes or until crisp-tender. Drain and rinse under cold running water; drain. Pat dry with paper towels.
Divide dough in half. Working with 1 half at a time (cover remaining dough to keep from drying), roll dough into an 11-inch circle on a lightly floured surface. Place dough on a baking sheet (or jelly-roll pan) sprinkled with 1 tablespoon cornmeal. Spread half of garlic mixture over dough. Top with 1/2 cup onion mixture and 3/4 cup asparagus, leaving a 1-inch border. Sprinkle with 6 tablespoons cheese. Slide topped dough onto preheated pizza stone, using a spatula as a guide. Bake at 500° for 8 minutes or until cheese melts and crust is golden brown. Remove from pizza stone using pizza peel. Place pizza on a cutting board; sprinkle with 1/8 teaspoon salt. Cut into 6 wedges. Repeat procedure with remaining dough, 1 tablespoon cornmeal, garlic mixture, 1/2 cup onion mixture, 3/4 cup asparagus, 6 tablespoons cheese, and 1/8 teaspoon salt.