1. Place chicken stock or broth in a pan and bring to a boil. Reduce to about 1 cup. While liquid is reducing, in a 3- to 4-quart sauté pan melt butter over medium heat. Add onion, carrot, celery, and garlic, and sauté until golden brown. Add balsamic vinegar and wine, scraping all the caramelized goodness off the bottom of the pan. Add thyme, increase heat to a boil, and reduce until most of the liquid has evaporated. Then add reduced stock and mix. Remove from heat and strain through a fine sieve. Reserve. (This sauce base can be made ahead and refrigerated; reheat before proceeding with recipe.)

2. Season both sides of each chicken breast with salt and pepper. Heat a large frying pan to medium-high. (The pan should be large enough to hold all the chicken in a single layer without overcrowding. If you do not have a pan large enough, use two pans, or cook in separate batches.) Pour a little oil into the pan and add chicken, skin side down. Cook until skin is crisp and golden, 5–6 minutes. Turn and cook through, another 2–3 minutes. When cooked, remove chicken from pan and keep warm.

3. In the same frying pan, add about 2 tablespoons olive oil. Add mushrooms and sauté for about 5 minutes. Add a pinch of salt (this helps mushrooms to release their excess water). Cook until golden.

4. Add reserved sauce base to mushrooms. Bring to a boil, reduce heat, and simmer for about 2 minutes, until reduced to about 1 cup liquid. Remove from heat and stir in mascarpone cheese. (Don’t worry about dissolving all the mascarpone; it’s nice to have some pieces melting over the chicken as it goes to the table.) Taste sauce and adjust seasoning. Pour sauce over chicken and serve.