Cover over med.-high heat, stirring frequently, until golden brown.
Remove chicken from skillet; set aside.
In same skillet, heat remaining 2 tsp oil; add mushrooms and onion. Cook stirring frequently, until all liquids has evaporated and onions are golden brown.
In small bowl, with wire whisk, combine broth and flour, blending until flour is dissolved; strain and add to skillet. Stirring constantly, bring liquid to a boil over high heat; reduce heat to low. Simmer 10 minutes, stirring frequently.
Stir reserved chicken into broth mixture; simmer 5 minutes.
Remove skillet from heat; stir in sour cream, red wine vinegar, mustard, and pepper.