Heat 1 tablespoon olive oil and 50 g butter in a large pan over medium-high heat. Season 6 chicken fillets with salt and pepper and add them to the pan along with garlic cloves separated from 1 bulb. Fry for 10 minutes until the chicken is browned. Deglaze with 2 tablespoons balsamic vinegar and simmer for 2 minutes. Add 175 ml Marsala and 175 ml hot chicken stock. Cover and simmer gently over medium heat for 20 minutes, turning the chicken once, until cooked through.
Remove the chicken from the pan and keep it warm. Strain the sauce through a sieve into a clean pan. Press the softened garlic cloves through the sieve back into the sauce. Stir in 4 tablespoons mascarpone until combined. Simmer for 2 minutes. Serve the chicken with the sauce spooned over it.