Pat the chicken thighs dry with paper towels. Season both sides with kosher salt and black pepper.
Heat olive oil in a large skillet over medium-high heat until shimmering.
Place the chicken thighs skin-side down in the skillet and cook without moving for 6-7 minutes until the skin is golden brown and crispy.
Flip the chicken thighs and cook for an additional 6 minutes. Remove the chicken from the skillet and set aside on a plate.
Reduce heat to medium. Add the sliced mushrooms to the skillet and sauté for 5 minutes until they release their moisture and begin to brown.
Add the chopped onion and cook for 3 minutes until softened.
Stir in the minced garlic and cook for 30 seconds until fragrant.
Pour in the white wine and scrape the bottom of the skillet with a wooden spoon to loosen any browned bits. Let the wine reduce by half, about 3 minutes.
Add the chicken broth, heavy cream, dried thyme, and smoked paprika. Stir to combine and bring the sauce to a gentle simmer.
Return the chicken thighs to the skillet, skin-side up. Spoon some sauce over the chicken.
Reduce heat to low, cover the skillet, and simmer for 10-12 minutes until the chicken is cooked through and reaches an internal temperature of 165°F (74°C).
Remove the chicken thighs from the skillet and set aside. Stir the unsalted butter into the sauce until melted and smooth.
Taste the sauce and adjust seasoning with additional salt and pepper if needed.
Return the chicken to the skillet, spoon sauce over the top, and sprinkle with chopped fresh parsley before serving.