Pat the chicken thighs dry with paper towels and season generously with salt and freshly ground black pepper on both sides. Drying the chicken ensures a crispy skin during searing.

Heat the olive oil and butter in a large deep skillet or Dutch oven over medium-high heat. Add the chicken thighs skin-side down and sear until golden brown and crispy, about 6 to 8 minutes per side. Transfer the chicken to a plate, leaving the flavorful fat in the pan.

Add the quartered mushrooms and diced onion to the skillet. Cook, stirring occasionally, until the mushrooms are browned and the onions have softened and turned translucent, about 5 to 7 minutes.

Stir in the minced garlic and dried thyme, cooking until fragrant, about 30 seconds. Pour in the dry white wine to deglaze the pan, using a wooden spoon to scrape up all the delicious browned bits from the bottom.

Add the undrained diced tomatoes, chicken broth, and halved green olives to the skillet. Stir well to combine and bring the mixture to a gentle, steady simmer.

Return the chicken thighs, along with any resting juices from the plate, back to the skillet. Nestle them into the tomato sauce, keeping the crispy skin above the liquid. Reduce the heat to medium-low, cover loosely, and let simmer for 25 to 30 minutes, or until the chicken is cooked through and tender.

Remove the skillet from the heat and sprinkle with fresh chopped parsley. Serve hot alongside thick slices of crusty garlic bread or over a bed of pasta to soak up the rich, savory sauce.