Heat olive oil in a large skillet over medium heat.
Season chicken thighs with salt and pepper, then add them to the skillet, skin side down.
Sear the chicken for about 6-7 minutes until golden brown, then flip and cook for another 5 minutes.
Remove the chicken from the skillet and set aside.
Add onions and cook until soft, about 3-4 minutes, then add garlic and mushrooms; sauté until mushrooms are tender.
Sprinkle flour over the vegetables and stir, cooking for 1-2 minutes.
Gradually stir in the chicken broth, scraping up any fond from the skillet.
Add the seared chicken back to the skillet, skin side up, and bring to a simmer.
Cover the skillet, reduce heat, and simmer for 20-25 minutes until the chicken is cooked through.
Remove the chicken again, then stir in the heavy cream and return to a gentle simmer.
Return the chicken once more, simmer for an additional 5-10 minutes; adjust seasoning if necessary.
Garnish with fresh parsley before serving.