Heat 1 Tbsp Oil in a large nonstick skillet over medium-high heat.
Sprinkle chicken with 1/2 tsp Pepper and 1/4 tsp Salt.
Add chicken to pan, cook until done, about 4 minutes per side.
Remove Chicken from pan (Do NOT wipe out pan)
Add remaining 1 Tbsp Oil to pan. Add Mushrooms and Thyme Sprigs; cook, stirring occasionally, until Mushrooms are browned, about 6 minutes.
Sprinkle flour over mixture, cook stirring constantly, 1 minute.
Add Stock and Wine to pan. Bring to a boil and cook until slightly thickened, 2-3 minutes.
Remove pan from heat, stir in butter, remaining 1/4 tsp Pepper and remaining 1/4 tsp Salt.
Add Chicken to pan, turning to coat.
Discard Thyme Sprigs before serving, sprinkle with chopped Thyme if desired.