Dry the chicken thoroughly with paper towels, season both sides with 1 1/2 teaspoons salt, and warm the olive oil over medium heat in a 6-quart skillet or Dutch oven. The oil should look fluid and shimmer lightly before the chicken goes in.

Arrange the thighs skin-side down and cook for 5 to 7 minutes, then turn and cook the second side for 2 minutes before moving them to a plate. The skin should be deep golden, while the centers will still need time to finish cooking.

Add the onion and bell pepper strips to the skillet and cook for 8 minutes. They should soften and pick up the browned flavor left in the pan.

Stir in the garlic, thyme, and mushrooms, then cook for 5 minutes. The mushrooms should soften and the garlic should smell fragrant without darkening.

Pour in the red wine over medium-high heat and cook for 3 to 5 minutes, scraping the browned bits from the pan, then add the broth, diced tomatoes, oregano, black pepper, red pepper flakes, and remaining 1/2 teaspoon salt. When the wine has reduced somewhat, nestle the chicken over the vegetables and spoon the liquid over each thigh.

Bring the skillet to a boil over high heat, then cover, lower the heat, and simmer for about 35 minutes. Listen for a quiet, steady simmer rather than a hard boil, and cook until the chicken is very tender and reaches the stated minimum temperature.

Uncover the skillet, lift the chicken onto a large plate with tongs or a slotted spoon, and remove the skin. Set the chicken aside while the sauce finishes concentrating.

Stir the olives into the sauce and simmer uncovered over medium-low heat for 15 minutes. The sauce is ready when it looks thicker and coats a spoon instead of running off quickly.

Return the chicken to the skillet, spoon the sauce over the thighs, and finish with parsley if using. The chicken should sit in a glossy sauce with softened vegetables and olives throughout.