Place top oven rack in the center position and pre-heat oven to 425°F.
Add one tablespoon extra virgin olive to a large cast iron skillet set over medium-high heat. Lightly season chicken thighs with salt and black pepper and add to hot skillet. Cook until the skin is nicely browned and releases easily from the bottom of the skillet, approximately 5-6 minutes.
Flip and cook another 4-5 minutes on the remaining side. Transfer chicken to a platter and set aside.
Reduce heat to medium and add remaining tablespoon olive oil to skillet. Add garlic and shallot and sauté, stirring continually, for 1-2 minutes or just until the shallot softens and develops some color.
Add the white wine and deglaze the skillet by gently scraping with a plastic spatula to release any browned bits from the bottom.
Add the olives, tomatoes, capers, herbes de Provence, and chicken broth to the skillet and stir to combine. Cook, stirring occasionally, just until heated through, approximately 1-2 minutes.
Remove from heat and nestle the chicken thighs in amongst the olive and tomato mixture. Transfer the skillet to the preheated oven and cook for 20-25 minutes, or until an instant-read thermometer reads just over 160°F when inserted into the thickest part of the meat (but not touching the bone).
Remove from oven and loosely cover the skillet with foil for 5 minutes before serving. Enjoy!