Prepare the Chicken: Preheat your oven to 400°F (200°C). Slice each chicken breast horizontally to create two thin cutlets. Place the cutlets between two sheets of parchment paper and gently pound them to a uniform ¼-inch thickness. In a small bowl, combine the oregano, thyme, paprika, kosher salt, and black pepper. Pat the chicken cutlets thoroughly dry with paper towels and season both sides evenly with the spice mixture.
Sear for Flavor: Heat 2 tablespoons of the extra virgin olive oil in a large, oven-safe skillet over medium-high heat. Once the oil shimmers, carefully place the seasoned chicken cutlets in the pan in a single layer (work in batches if necessary to avoid crowding). Sear for 2-3 minutes per side, until a golden-brown crust forms. The chicken will not be fully cooked. Transfer the seared chicken to a plate and set aside.
Build the Sauce: Reduce the skillet heat to medium. Add the remaining 1 tablespoon of olive oil. Add the sliced garlic and sauté for 30-60 seconds until fragrant, being careful not to let it burn. Pour in the dry white wine to deglaze, scraping up any browned bits from the bottom of the pan with a wooden spoon. Allow the wine to simmer and reduce by about half, about 1-2 minutes.
Combine and Braise: Turn off the heat. Stir in the lemon juice, rinsed capers, and the drained artichoke hearts. Arrange the seared chicken cutlets back into the skillet, nestled amongst the artichokes. Spoon some of the sauce and garlic over the chicken. Transfer the skillet to the preheated oven and bake, uncovered, for 10-12 minutes, or until the chicken is cooked through and the internal temperature reaches 165°F (74°C).
Finish and Serve: Carefully remove the hot skillet from the oven. Scatter the fresh spinach over the top; the residual heat will cause it to wilt perfectly in about a minute. Garnish the entire dish generously with the reserved lemon zest and freshly chopped parsley. Serve immediately.