Preheat the oven to 375°F (190°C). Lightly grease a baking dish or line it with parchment for easy cleanup.
Pat the chicken breasts dry. Using a sharp knife, carefully slice a pocket into the side of each breast—be sure not to cut all the way through. You want a reasonable opening for stuffing.
In a skillet over medium heat, warm 1 tablespoon of olive oil. Add the chopped mushrooms and a pinch of salt. Sauté until they release their moisture and begin to brown, about 5–7 minutes. Add the minced garlic and cook for another 30 seconds until fragrant.
Remove the skillet from heat. Stir in the breadcrumbs, parmesan, parsley, thyme, spinach, and a pinch of salt and pepper. The mixture should be cohesive enough to spoon into the chicken pockets.
Divide the stuffing evenly among the four pockets. Use toothpicks to seal the openings if needed to prevent spilling during cooking.
In the same skillet, heat the remaining tablespoon of olive oil over medium heat. Lightly brown the stuffed chicken on all sides, about 2 minutes per side.
Transfer the chicken to the prepared baking dish. Bake for 22–28 minutes, or until the chicken reaches an internal temperature of 165°F (74°C) and the stuffing is hot. If you like a crisper top, switch the oven to broil for the last 2–3 minutes—watch carefully so it doesn’t burn.
Let the chicken rest for a few minutes before serving. Slice open to reveal the savory filling and serve with a simple side salad or roasted vegetables.