Pat the salmon filets 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 salmon and cook until the salmon easily releases from the pan. Flip, then cook on the second side. Transfer to a plate.
To the same pan, melt unsalted butter, then add chopped shallot and season with Kosher salt. Cook, stirring occasionally, until translucent. Add chopped fresh basil, chopped sun-dried tomatoes, garlic, dried oregano, and crushed red pepper flakes. Cook.
Stir in tomato paste, then pour in dry white wine. Use a spatula to scrape up any browned bits off the bottom of the pan. Cook. Stir in mascarpone cheese and grated Parmesan, then add watercress. Squeeze half a lemon right on top, then stir well. Taste and adjust seasoning as needed.
Return the salmon to the pan (skin side up, if using skin-on). Garnish with additional fresh basil and watercress, then serve immediately with a pinch of flaky sea salt!