Heat the olive oil in a large skillet over medium heat.
Season the chicken thighs generously with salt and pepper, then place them skin-side down in the hot skillet.
Sear the chicken for about 5–7 minutes until golden brown, then flip and cook for another 5 minutes.
Remove the chicken from the skillet and set aside.
Add the diced onion, garlic, carrots, and mushrooms to the same skillet, stirring to coat in the residual fat.
Sauté the vegetables for about 5 minutes, or until they soften.
Sprinkle the flour over the sautéed vegetables and stir to combine, cooking for another 2 minutes.
Gradually whisk in the chicken broth, scraping up any bits stuck to the bottom.
Return the chicken thighs to the skillet, skin-side up, and let simmer for 30 minutes.
Once the chicken is cooked through, remove it and stir in the heavy cream and thyme.
Return the chicken to the skillet and let it simmer for an additional 5 minutes.
Garnish with fresh parsley before serving hot.