To prepare flatbread, dissolve sugar and yeast in 1/4 cup water in a large bowl; let stand 5 minutes. Lightly spoon flour into dry measuring cups and spoons; level with a knife. Add 1/4 cup flour to yeast mixture, stirring with a whisk. Cover and let stand 30 minutes (mixture will be bubbly); uncover. Add 1/2 cup plus 3 tablespoons water to yeast mixture. Add 1 3/4 cups flour, 1 tablespoon oil, and 1/2 teaspoon salt, stirring until a soft dough forms. Turn the dough out onto a floured surface. Knead until smooth and elastic (about 10 minutes); add enough of the remaining 3 tablespoons flour, 1 tablespoon at a time, to prevent dough from sticking to hands (dough will feel sticky).
Place dough in a large bowl coated with cooking spray, turning to coat top. Cover and let rise in a warm place (85°), free from drafts, 1 hour or until doubled in size. (Gently press two fingers into dough. If indentation remains, dough has risen enough.)
Punch dough down, and divide in half. Working with one portion at a time (cover remaining dough to prevent drying), roll each portion into a 12-inch circle on a floured surface. Place 1 dough circle on a pizza peel sprinkled with 1 tablespoon cornmeal.
Place a pizza stone on the bottom rack in oven. Preheat oven to 500°.
To prepare toppings, combine 2 1/2 teaspoons oil and garlic in a bowl; let stand 30 minutes.
Heat a large nonstick skillet over medium heat. Coat pan with cooking spray. Add spring onions and 1/4 teaspoon salt to pan. Cover and cook for 20 minutes, stirring occasionally. Uncover and cook for 3 minutes or until golden, stirring frequently.
Cook asparagus in boiling water 2 minutes or until crisp-tender. Drain; rinse under cold water. Drain.
Brush dough circle with half of the garlic mixture; arrange half of the asparagus and onion mixture over dough, leaving a 1/2-inch border. Top with half of shredded cheese. Slide dough onto preheated pizza stone. Bake at 500° for 9 minutes or until lightly browned. Repeat procedure with the remaining dough circle, cornmeal, garlic mixture, asparagus, onion mixture, and shredded cheese. Serve immediately.