Heat oil or margarine in a pan over medium-high heat. Add mushrooms, a pinch of salt, and a small amount of sugar. Fry for 3-5 minutes until mushrooms soften. Add creme fraiche and beef stock. Stir in fresh herbs and bring to a boil. Boil for 2 minutes, then reduce heat to medium. Simmer for 15 minutes, stirring occasionally. Season with salt, pepper, and lemon juice.
Combine herbal cream cheese and garlic cream cheese in a bowl. Stir in chopped parsley, chopped chives, and diced onion. Season with salt and pepper.
Butterfly each chicken breast by cutting almost all the way through horizontally, then opening like a book. Season inside with pepper. Spread filling generously onto one half, then fold the other half closed. Wrap each filled breast with bacon strips and secure with toothpicks if needed.
Heat oil or margarine in a large skillet over medium-high heat. Place bacon-wrapped chicken in the skillet. Cook for 15-20 minutes, turning occasionally, until bacon is crispy and chicken reaches 74°C / 165°F in the thickest part. Serve with sauce alongside pasta.