Begin by preheating your oven to 375°F (190°C).
Season the chicken breasts with salt and black pepper on both sides.
In a skillet, melt the unsalted butter over medium heat and add the sliced mushrooms. Sauté the mushrooms until they are browned and have released their moisture, which should take about 5-7 minutes.
Stir in the minced garlic and thyme leaves, cooking for an additional minute until fragrant.
Add the fresh baby spinach to the skillet and cook until wilted, about 2-3 minutes. Remove the skillet from heat and let the mixture cool slightly.
Once cooled, mix in the mozzarella cheese until well combined.
Carefully cut a pocket into each chicken breast and stuff them with the mushroom and spinach mixture.
Heat the olive oil in an oven-safe skillet over medium-high heat. Sear the stuffed chicken breasts for 3-4 minutes on each side until golden brown.
Transfer the skillet to the preheated oven and bake for an additional 20-25 minutes, or until the chicken is cooked through and reaches an internal temperature of 165°F (75°C).
Let the chicken rest for a few minutes before slicing and serving. Enjoy your delicious mushroom stuffed chicken breast!