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Marinate chicken breasts for at least 3 hours in fridge. Preheat oven to 350°F (180°C) with rack in middle position.
In a pan on high heat, melt 1 tbsp. (15 ml) butter and sear chicken breasts for 2 minutes on each side until golden. Season. Remove chicken breasts from pan and place in an ovenproof dish. Bake for about 25 minutes.
In a saucepan, fry onion in butter (15 ml) until caramelized, approximately 10 minutes. Add balsamic vinegar, honey, and salt. Cook 2 to 3 more minutes or until the mixture has a syrupy consistency.
Once chicken is cooked, remove from oven. Set oven to broil and roast two whole peppers, turning every 2 minutes. Remove from oven and set aside 5 minutes in a bowl covered with plastic wrap. Peel roasted peppers and cut into strips.
Whip Tartare cheese in a bowl.
Cut chicken into strips.
Assemble all ingredients and garnish with fresh herbs.