Season the chicken thighs with salt and pepper on both sides. This builds the flavor base for the entire dish.
In a large skillet, heat the olive oil over medium heat. Add the seasoned chicken thighs and sear until they are golden brown on each side, about 3 to 4 minutes per side. Remove the chicken and set it aside, leaving the flavorful browned bits in the pan.
Add the diced onion to the pan and sauté until it becomes translucent and starting to brown, about 4 minutes. Stir in the minced garlic and cook for another 30 seconds to wake up its aroma.
Toss in the sliced mushrooms and cook until they release their moisture and soften, about 5 minutes. If the pan looks dry, splash in a little broth to loosen the nice fond on the bottom.
Sprinkle the flour over the vegetables and stir to coat. Cook for 1 minute to remove the raw flour taste, creating a light roux that will thicken the gravy.
Pour in the chicken broth slowly, whisking as you go to prevent lumps. Return the chicken to the pan along with the thyme. Bring the mixture to a gentle simmer.
Stir in the heavy cream, letting the sauce simmer until it thickens to a rich, velvety gravy. Taste and adjust salt and pepper if needed.
Nestle the chicken back into the sauce, spooning some of the gravy over the top. Reduce heat to low and cook for about 5 to 7 minutes, or until the chicken is cooked through and the flavors have melded.
Finish with a knob of butter stirred in to add shine and silkiness. If you like, sprinkle fresh parsley for a bright finish.