Cook the asparagus in boiling water 3 minutes or until crisp-tender. Drain and set aside.
Combine 1 cup water, the wine, and broth in a small saucepan; bring to a simmer (do not boil). Keep warm over low heat.
Coat a medium saucepan with cooking spray; place over medium heat until hot. Add mushrooms, green onions, and garlic; sauté 2 minutes. Add rice; cook 1 minute, stirring constantly. Add 1/2 cup warm broth mixture and ham; cook 3 minutes or until liquid is nearly absorbed, stirring constantly. Add remaining broth mixture, 1/2 cup at a time, stirring constantly until each portion of broth is absorbed before adding the next (about 20 minutes total). Add asparagus during the last 4 minutes of cooking time. Remove from heat; stir in parsley and thyme. Serve immediately.