Prepare the Chicken: Cut chicken into 1-inch pieces, season with salt and pepper, and dredge in flour.
Cook the Chicken: Heat 2 tablespoons of olive oil in a skillet over medium-high heat. Cook chicken until browned, about 3 minutes per side. Set aside.
Sauté Vegetables: Add butter to the skillet, then sauté mushrooms and onions until mushrooms release their liquid and it evaporates, about 6-8 minutes.
Add Seasonings: Stir in dry mustard, Worcestershire sauce, and garlic. Cook for 1 minute.
Simmer with Broth: Pour in chicken broth, scraping up browned bits. Return chicken to the skillet and simmer.
Finish with Sour Cream: Reduce heat, stir in sour cream, and adjust seasoning. Serve over egg noodles or mashed potatoes.