Pat the chicken dry with paper towels, then season on all sides with Kosher salt and black pepper.
Heat neutral oil in a large skillet over medium-high heat. When hot, add chicken and cook on the first side, or until golden brown. The chicken should easily release from the pan. Flip, then continue cooking. Transfer to a plate.
To the same pan, melt unsalted butter, then add thinly sliced onion and season with Kosher salt. Cook, stirring occasionally, until translucent. Add chopped fresh basil, chopped sun-dried tomatoes, cloves of garlic, dried oregano, and red pepper flakes. Cook.
Stir in tomato paste, breaking up with a spatula until dissolved, then pour in dry white wine. Use a spatula to scrape up any browned bits off the bottom of the pan. Cook, then pour in low-sodium chicken broth. Bring to a boil. Stir in heavy cream, mascarpone cheese, and grated Parmesan.
Return the chicken to the pan, coating it on all sides in the sauce, then simmer or until the chicken is fully cooked. Garnish with fresh basil. Serve immediately with a pinch of flaky sea salt!