Combine the olive oil and half of the butter in a large skillet and heat over medium-high.
Add the chicken and cook for 5-7 minutes on each side, cooking until golden brown. Remove from the skillet and set aside.
Working in the same skillet, add the remaining butter and whisk in the flour over medium heat - cook for 1 minute.
Whisk in the chicken broth and white wine, bringing to a simmer. Reduce the heat, simmering for 5 minutes to thicken.
Stir in the heavy cream and seasonings, adding additional seasonings to taste.
Add the chicken back to the skillet and let it simmer in the gravy for 2-3 minutes until heated.
Serve over mashed potatoes, rice, or noodles.
Notes
TipsDon't overcrowd the pan, cook in batches if necessary.Deglaze to add flavor using a wooden spoon to scrape up any browned bits from the bottom of the pan.