Season chicken breasts with salt and pepper, then dredge lightly in flour, shaking off excess.
Heat olive oil in a large skillet over medium-high heat. Sear chicken for 5 to 7 minutes per side until internal temperature reaches 165 degrees Fahrenheit. Remove chicken from skillet and set aside.
Add butter to the same skillet. Sauté mushrooms and onions for 8 to 10 minutes until mushrooms are browned and liquid has evaporated.
Add garlic and thyme, cooking for 60 seconds until fragrant.
Pour in white wine to deglaze the skillet, scraping the bottom to release browned bits. Simmer until liquid is reduced by half.
Stir in heavy cream and bring to a low simmer. Continue cooking for 3 to 5 minutes until the sauce thickens.
Stir in parmesan cheese until melted and incorporated.
Return chicken breasts to the skillet and spoon the mushroom sauce over the top. Simmer for 2 minutes to heat through before serving.