Lightly season the chicken breasts on both sides with salt, pepper, and thyme. Place them in a greased baking dish.
In a bowl, combine softened cream cheese, garlic, oregano, and half of the mozzarella cheese. Mix until well combined.
Stir the chopped spinach into the cream cheese mixture until evenly distributed.
Spread the cream cheese mixture evenly over the chicken breasts in the baking dish.
Scatter the halved cherry tomatoes on top of the cream cheese layer.
Drizzle olive oil over everything, then cover the dish with foil and bake in the preheated oven for 25 minutes.
Remove the foil, sprinkle the remaining mozzarella over the top, and return to the oven uncovered for an additional 15 minutes, or until the chicken is cooked through and the cheese is bubbly and golden.
Once done, remove from the oven, let it rest for a few minutes, then garnish with fresh parsley before serving.
Notes
Let the dish rest before serving for better flavor.