Heat oil in 10" nonstick skillet. Saute asparagus, ham, garlic and green onion over medium-high heat until asparagus is crisp tender, about 8 minutes.
Whisk together eggs, cheese, salt and pepper in a large bowl. Pour into skillet with asparagus mixture and stir to distribute egg mixture through skillet. Cook without stirring until edges are just set, about 2 minutes.
Transfer skillet to oven; bake until center is set, about 30 minutes. Cut into wedges and serve.