Preheat the oven to 375°F (190°C). Using a sharp knife, carefully cut a pocket into the side of each chicken breast, making sure not to slice all the way through. Pat the chicken dry with paper towels, then season the outside and inside with salt, pepper, and fresh thyme.
In a medium mixing bowl, combine the softened cream cheese, thawed and squeezed spinach, chopped artichoke hearts, mozzarella cheese, parmesan cheese, minced garlic, and heavy cream. Mix until well combined.
Stuff each chicken breast pocket evenly with the spinach and artichoke filling. Use toothpicks to secure the openings so the filling remains inside during cooking.
Heat the olive oil in a large oven-safe skillet over medium-high heat. Add the stuffed chicken breasts and sear for 4 to 5 minutes on each side until a golden brown crust forms.
Transfer the skillet to the preheated oven and bake for 15 to 20 minutes, or until the chicken reaches an internal temperature of 165°F (74°C). Remove from the oven, let rest for 5 minutes, discard the toothpicks, and serve warm.