Season the chicken thighs with salt and pepper on both sides. In a large skillet, heat 1 tablespoon of olive oil over medium-high heat. Add the chicken breasts and cook until golden brown on both sides and cooked through, about 5-6 minutes per side depending on thickness. Remove the chicken from the skillet and set aside.

In the same skillet, add 1 tablespoon butter along with the mushrooms. Cook about 5 minutes. Next, add another tablespoon of butter along with the shallots and garlic. Sauté until fragrant and translucent, about 2-3 minutes.

Sprinkle the flour over the mushrooms and stir to combine. Cook for an additional minute to cook off the raw flour taste. Slowly pour in the white wine and chicken broth, stirring constantly to avoid lumps. Bring the sauce to a simmer and let it cook for 5-7 minutes or until slightly thickened.

Return the chicken thighs to the skillet, nestling them into the sauce. Let them simmer in the sauce for another 5 minutes to heat through and soak up the flavors. Taste the sauce and adjust the seasoning with salt and pepper if needed.

Serve the mushroom chicken with wine sauce hot, over mashed potatoes or rice. Garnish with chopped fresh parsley before serving.