Season chicken cutlets with salt and black pepper on both sides.
Heat large skillet over medium heat. Add vegetable oil. Once oil is heated, bring chicken cutlets to skillet, avoid overlapping. Once one side of the chicken cutlet is cooked and slightly golden brown, flip to cook the other side.
Once chicken is fully cooked, remove from heat and set aside.
Keep skillet on medium heat, add butter, then add garlic and mushrooms. Sear for 1 minute or until mushrooms soften.
Add flour, stir to combine, about ~30 seconds.
Add white wine. Some of the wine would evaporate when it touches the skillet. Stir to combine, about 1 minute.
Add half and half. Stir/whisk to combine and dissolve flour completely. Bring to a boil.
Lower heat and let sauce simmer for 2-3 minutes, or until sauce thickens to desired consistency and alcohol evaporates (there shouldn't be a strong alcoholic taste in the sauce after alcohol evaporates). (See Note 2)
Add 1/2 tsp salt and 1/4 tsp pepper to the sauce, or to taste. Stir to combine.
Add chicken back into the sauce. Spoon sauces over the chicken. Switch off heat. Garnish with parsley.
Serve and enjoy!