Season the chicken with a generous pinch of salt and pepper. In a large, heavy skillet heat the olive oil over medium heat. Add the chicken and cook until it browns, then turn to brown the other side as well. This should take about 4 minutes per side, depending on how thick the chicken is. When both sides are well browned, remove chicken from pan and set aside. Don’t worry about the chicken being fully cooked because you will be adding it back to the pan to finish cooking it.
In the same skillet, melt 2 tablespoons over medium high heat. Add the onion and sauté for about 3 minutes. Add the mushrooms and garlic and sauté until the mushrooms are tender and the juices evaporate. This should take about 10-12 minutes.
Once the mushrooms are tender, add the wine and simmer until the liquid is reduced by half, about 5 minutes. Whisk in mascarpone and mustard. I like to use a whisk instead of a spoon to better incorporate the mascarpone and mustard.
Add the chicken back to the skillet, along with any juices that accumulated. Simmer over medium-low heat until the chicken is cooked through and the sauce thickens, about 2-5 minutes.
Sprinkle with parsley and, if needed, season with an extra pinch of salt and pepper.
Serve immediately.