Pat chicken thighs dry with paper towels and season thoroughly with salt and black pepper.

In a large heavy-bottomed Dutch oven or deep skillet, heat the olive oil and 1 tablespoon of butter over medium-high heat. Sear the chicken in batches until deeply browned on all sides (about 4-5 minutes per side). Remove chicken and set aside on a plate.

Reduce heat to medium. Add the remaining 2 tablespoons of butter, sliced onions, bell peppers, and mushrooms. Sauté for 8-10 minutes until the vegetables have softened and the mushrooms have released their moisture.

Add the minced garlic and cook for 1 minute until fragrant.

Stir in the tomato paste and cook for 3-4 minutes, stirring constantly, until the paste turns a deep brick-red color (the 'pincer' technique) to develop depth of flavor.

Deglaze the pan with the white wine, scraping the bottom with a wooden spoon to release all the browned bits (fond). Let the wine reduce by half.

Add the crushed tomatoes, chicken stock, and dried oregano. Stir to combine and return the browned chicken and any accumulated juices to the pot.

Bring the sauce to a gentle boil, then reduce heat to low. Cover and simmer for 35-40 minutes until the chicken is fork-tender and the sauce has thickened.

While the sauce simmers, cook the pasta in a large pot of heavily salted boiling water until 1 minute short of al dente.

Stir the olives and capers into the sauce during the last 5 minutes of simmering.

Transfer the pasta directly into the sauce using tongs. Add a splash of pasta water if the sauce is too thick. Toss for 1-2 minutes over medium heat to allow the pasta to finish cooking in the sauce.

Remove from heat, garnish with fresh parsley, and serve immediately with optional grated Pecorino Romano.