Wash duck breasts and pat dry. Cut skin crosswise, season with salt and pepper. Fry in hot oil for 15-20 minutes, turning. Meanwhile peel and wash the carrots. Cook in boiling salted water for about 12 minutes.
Remove duck breast and keep warm. Add sesame seeds and honey to the cooking fat. Deglaze with vinegar, bring to the boil briefly. Add chicken stock, cook over high heat for 2 minutes. Cut butter into small cubes and stir in little by little. Do not let it boil any more! Season again with salt and pepper. Cut open duck breast. Arrange on plates with sauce and vegetables.
Cut butter into small cubes and stir in little by little. Do not let it boil any more! Season again with salt and pepper. Cut open duck breast. Arrange on plates with sauce and vegetables. Serve garnished with lemon and mint