Lightly season the chicken breasts with sea salt and black pepper on both sides.
In a large sauté pan over medium-low heat, melt 2 tablespoons butter. Add the sliced onions and cook slowly until deeply caramelized, about 30 minutes. Remove onions and set aside.
Increase heat to medium-high. Add the remaining 3 tablespoons butter and sear the chicken breasts until golden brown on both sides. Remove from the pan and set aside.
Deglaze the pan with chicken stock. Use a rubber spatula to scrape up all the flavorful browned bits from the bottom of the skillet. Simmer for 5 minutes.
Reduce heat to medium-low and add heavy cream, Parmesan cheese, balsamic vinegar, mushrooms, and a little salt and pepper.
Simmer the sauce for 10 minutes, stirring occasionally, until thickened and reduced by half.
Add the chicken and caramelized onions back into the skillet. Continue simmering until the chicken reaches an internal temperature of 165°F, about 10 minutes.
Garnish Pan Seared Chicken with Balsamic Cream Sauce with fresh parsley before serving.