Season the chicken breasts on both sides with salt, pepper, and garlic powder.
Heat the olive oil in a large oven-safe skillet over medium-high heat.
Sear the chicken for 5 to 7 minutes per side until golden brown and the internal temperature reaches 165°F (74°C). Transfer chicken to a plate and keep warm.
In the same skillet, melt the butter over medium heat. Add the mushrooms and sauté for 5 to 6 minutes until browned and tender.
Add the minced garlic and cook for 1 minute until fragrant.
Deglaze the skillet with chicken broth, scraping up any browned bits from the bottom.
Stir in the heavy cream and dried thyme. Simmer the sauce for 3 to 4 minutes until slightly thickened.
Return the chicken breasts to the skillet and spoon the mushroom sauce over them.
Top each chicken breast with a slice of Swiss cheese.
Cover the skillet with a lid for 2 minutes, or place under a broiler for 1 minute, until the cheese is completely melted and bubbly.
Garnish with chopped parsley before serving.