In a large bowl, whisk together 3 tablespoons Greek yogurt, 1/4 teaspoon minced garlic, 2 tablespoons artichoke jar liquid, and a pinch of salt and pepper to make the marinade.
Place the chicken breasts in the bowl and spoon the marinade over them to coat. Cover and refrigerate for at least 2 hours.
When ready to cook, preheat your grill to medium-high heat.
Use a sharp knife to slice a pocket into the side of each chicken breast, taking care not to cut through the other side.
Stuff each pocket with 2–3 spinach leaves (about 8–10 leaves total across breasts) and one small drained artichoke heart. Secure openings with toothpicks and sprinkle the outside with a pinch of Italian seasoning.
Grill the stuffed chicken until cooked through and no longer pink in the middle, about 6–7 minutes per side, flipping once.
Transfer chicken to a plate and cover; let rest for 10 minutes.
While the chicken rests, combine 1/2 cup Greek yogurt, the remaining 4 small drained artichoke hearts, 1 teaspoon minced garlic, and 1/3 cup grated Parmesan in a small food processor; blend until smooth, scraping down the sides as needed. Season with salt and pepper to taste.
Spoon the creamy artichoke–Greek yogurt sauce over the rested chicken and serve.