Preheat your oven to 375°F (190°C).
In a skillet over medium heat, add 1 tablespoon of olive oil. Sauté the chopped mushrooms and minced garlic until the mushrooms are soft and any moisture has evaporated, about 5-7 minutes.
In a mixing bowl, combine the sautéed mushrooms, cream cheese, Parmesan cheese, breadcrumbs, dried thyme, salt, and black pepper. Mix until well combined.
Carefully slice a pocket into each chicken breast, making sure not to cut all the way through.
Stuff each chicken breast with the mushroom mixture, securing the opening with toothpicks if necessary.
Heat the remaining tablespoon of olive oil in the skillet over medium-high heat. Sear the stuffed chicken breasts for 3-4 minutes on each side until golden brown.
Transfer the seared chicken breasts to a baking dish and bake in the preheated oven for 20-25 minutes, or until the chicken is cooked through and reaches an internal temperature of 165°F (75°C).
Remove from the oven, let rest for 5 minutes, then garnish with fresh parsley before serving.