Season chicken thighs evenly with salt and black pepper on both sides.
Heat olive oil in a large skillet over medium-high heat and sear chicken for 6-8 minutes per side until the internal temperature reaches 165°F.
Remove chicken from the skillet and set aside on a plate.
In the same skillet, melt butter and add sliced mushrooms; sauté for 8 minutes until browned and moisture has evaporated.
Add diced onion and minced garlic to the mushrooms and cook for 3 minutes until softened.
Sprinkle gluten-free flour over the vegetables and stir constantly for 2 minutes to cook out the raw flour taste.
Slowly whisk in the chicken broth, scraping the bottom of the pan to deglaze and incorporate any browned bits.
Simmer the mixture for 5 minutes until the sauce has thickened into a soup-like consistency.
Reduce heat to low and stir in the heavy cream and fresh thyme leaves.
Return the cooked chicken thighs to the skillet, spooning the mushroom soup base over the chicken to smother.
Garnish with fresh parsley and serve immediately.