Pre-heat the oven to 400 degrees Fahrenheit. Line a baking sheet with parchment paper and set it aside.
Place the butter in a skillet and melt over med-high heat. Add the mushrooms and cook, stirring occasionally, for about 5 minutes. Add ¼ teaspoon salt, ¼ teaspoon pepper, ¼ teaspoon thyme, the parsley, and the minced garlic and stir to combine. Cook for another 30-60 seconds until the garlic is fragrant. Remove from heat.
Place the chicken breasts on a cutting board. Using a sharp knife, slice the breasts from the side (creating a top and bottom) almost all the way through. In a small dish, combine the remaining ½ teaspoon salt, ¼ teaspoon pepper, ¼ teaspoon thyme, and ¼ teaspoon garlic powder and stir together. Keeping the chicken breasts folded shut, sprinkle the seasoning over the tops of the breasts and flip over to sprinkle over the bottoms. Flip the breasts back over and open them up.
With each breast open at the slit, sprinkle the shredded Parmesan and Mozzarella cheeses evenly between the breasts, placing it on one side the open chicken. Arrange the sauteed mushrooms over top of the cheese layer on each breast. Close the breasts, folding the top half back over the mushrooms and cheese and press it down.
In a large skillet, add the olive oil and bring over medium-high heat (if your skillet or sauté pan doesn’t fit all four breasts, just cook two breasts at a time with 1 ½ teaspoons of oil each round). *Add the stuffed chicken breasts to the pan and cook for about 1 minute until the bottoms are golden. Flip the breasts and cook for another minute on the other side. *This step might get messy! If some of your mushrooms fall out into the pan when transferring, searing, or flipping, don’t worry! You can always stuff the stray mushrooms back in once you transfer the breasts to the baking sheet before putting it in the oven. Transfer the breasts to the prepared baking sheet and stuff any errant mushrooms back in if needed. Place in the pre-heated oven. Bake for 20-24 minutes until chicken is fully cooked through.