Combine flour, thyme, 1/8 teaspoon salt, and 1/4 teaspoon pepper; set aside 2 tablespoons flour mixture.
Place each piece of veal between 2 sheets of plastic wrap; flatten to 1/4-inch thickness, using a meat mallet or rolling pin.
Combine veal and flour mixture in a large zip-top plastic bag; seal bag, and shake to coat veal.
Heat a large nonstick skillet over medium heat. Coat half of veal pieces with cooking spray; add to skillet. Cook 1 minute on each side or until browned. Remove veal from skillet. Set aside, and keep warm. Repeat procedure with remaining veal.
Add 2 teaspoons butter to skillet; cook mushrooms and onion 2 minutes, stirring constantly. Add wine, scraping skillet to loosen browned bits; simmer 2 minutes.
Whisk together beef broth and reserved 2 tablespoons flour mixture; stir into mushroom mixture. Simmer 5 minutes, stirring constantly. Remove from heat; stir in sour cream.
Cook spaetzle according to package directions, omitting salt and fat; drain well. Melt remaining 1 teaspoon butter in a large nonstick skillet over medium-high heat; add spaetzle. Sprinkle with remaining 1/8 teaspoon salt and 1/4 teaspoon pepper; cook, stirring constantly 3 minutes or until lightly browned. Place spaetzle in a serving dish; top with veal and sauce.