Thoroughly pat the salmon fillets dry with paper towels to ensure a crisp sear. Season both sides of the fillets evenly, including the flesh and skin, with 1 teaspoon of the salt and freshly cracked black pepper.

Heat the sun-dried tomato oil in a large 30cm skillet over medium-high heat until shimmering. Place salmon fillets skin-side down, pressing down gently with a flat spatula for 10 seconds to maximize contact. Sear undisturbed for 5 minutes until skin is golden brown and crisp, then flip and cook for 3 to 4 minutes until the internal temperature registers 63 °C (63 °C) for safe, tender flakiness. Transfer skin-side up to a warm plate.

Reduce heat to medium and melt the butter in the same skillet. Add minced shallot and cook for 2 to 3 minutes until translucent and fragrant, scraping up any rendered browned fond from the bottom of the pan.

Stir in the chopped sun-dried tomatoes, tomato paste, minced garlic, and red pepper flakes. Toast and stir for 1 minute until fragrant and the tomato paste deepens in color.

Pour in the low-sodium broth, heavy cream, and the remaining 0.5 teaspoon salt. Bring the mixture to a gentle simmer over medium heat, scraping the skillet bottom. Simmer uncovered for 3 to 4 minutes until velvety and slightly reduced.

Remove skillet from heat. Whisk in freshly grated Parmigiano-Reggiano a handful at a time until silky and completely emulsified. Nestle salmon fillets back into the skillet with the crispy skin resting above the sauce. Garnish with fresh basil and serve immediately.