Steam asparagus until crisp-tender, about 5 minutes. Drain.
Whisk eggs, grated Parmesan cheese, 1/2 teaspoon salt and 1/4 teaspoon pepper in large bowl to blend well. Sauté bacon pieces in heavy large nonstick skillet over medium-high heat until golden brown, about 3 minutes. Add sliced green onions and sauté until onions are translucent, about 3 minutes. Add cooked asparagus; sauté until heated through. Reduce heat to medium. Spread asparagus mixture in single layer in skillet. Pour egg mixture over asparagus. Cook until eggs are very softly set, tilting skillet, gently running rubber spatula around edges and allowing uncooked egg portion to flow underneath, about 4 minutes. Tilt skillet and slide omelet out onto plate, folding omelet in half. Cut omelet into wedges and serve.