Preheat your oven to 375°F (190°C).

Make a pocket in each chicken breast by cutting along the side. Be careful not to cut all the way through. Season the outside and inside of the chicken breasts with salt and pepper.

In a skillet over medium heat, add 1 tablespoon olive oil, garlic, and mushrooms. Cook until mushrooms are browned, about 5 minutes. Add thyme and season with salt and pepper. Remove from heat and let it cool slightly.

Stuff each chicken breast pocket with the mushroom mixture, and then insert a slice of Swiss cheese into each pocket. Secure with toothpicks if necessary.

In the same skillet, heat the remaining olive oil over medium-high heat. Sear the chicken breasts until golden, about 3 minutes per side.

Transfer the skillet to the oven, or place the chicken breasts in a baking dish if your skillet isn't oven-safe, and bake for 20 minutes or until the chicken is cooked through. The internal temperature should read 165°F (74°C) when it’s ready.

Let the chicken rest for a few minutes before serving to keep those juices locked in. Serve hot, garnished with additional thyme if desired.