Steps
1. Season the chicken with salt and pepper. Heat the olive oil in a small skillet over medium heat and brown the chicken on both sides, about 3 minutes per side; transfer to a plate.
2. Add the shallot and mushrooms to the skillet. Cook, stirring, until the mushrooms soften and begin to brown, about 4 minutes.
3. Pour in the red wine and scrape up the browned bits. Simmer until reduced by about half, around 3 minutes.
4. Add the chicken and 60 ml broth. Cover and simmer gently until the chicken is cooked through and tender, about 12–15 minutes. Stir in the thyme and butter.
5. Meanwhile, bring the remaining 120 ml broth and 120 ml water to a boil in a small saucepan. Slowly whisk in the polenta and cook, stirring, according to its package timing, until smooth and thick. Stir in the Parmesan and season to taste.
6. Spoon the polenta into a bowl and top with the chicken, mushrooms, and wine sauce.