In a large skillet, cook and stir onion in hot butter and oil until tender.
Add mushrooms. Cook and stir until mushrooms have released all of their juices and are dry.
Add garlic. Cook 1 minute. Cool.
In a medium bowl, combine goat cheese, spinach, egg, thyme, oregano, salt and pepper. Stir in mushroom mixture. Set aside.
Place the chicken breasts one at a time between parchment paper. Gently pound with a mallet until ¼” thick. Place the chicken breasts one at a time between parchment paper. Gently pound with a mallet until ¼” thick.
Lightly season flesh side with salt and pepper.
Pre-heat conventional oven to 375 F.
Place ¼ c. of the spinach mixture in the center of the flesh side of each chicken breast. Roll up. Secure with toothpicks.
Bake at 375 F. for 25 Minutes
Meanwhile, in a saucepan, gently heat and stir the goat cheese and heavy cream until smooth and warm.
To serve, spoon 3 Tbsp. over each chicken breast