Pat salmon fillets completely dry with a paper towel and season both sides generously with salt and pepper. Heat olive oil and butter in a large skillet over medium-high heat. Once the butter is foaming, place salmon in the skillet and sear for 4-5 minutes, undisturbed, until a golden-brown crust forms. Flip and cook for another 3-4 minutes. Remove salmon to a plate.

Reduce heat to medium. Add minced garlic and cook for 30 seconds until fragrant. Add the chopped sun-dried tomatoes and crushed red pepper flakes and sauté for another minute.

Pour in the broth to deglaze, scraping up any browned bits. Simmer for 2-3 minutes until reduced by half. Reduce heat to low and whisk in the heavy cream. Simmer gently for 3-4 minutes until it starts to thicken. Turn off the heat and stir in the Parmesan cheese until smooth, followed by the fresh basil ribbons.

Return the seared salmon to the skillet, nestling it into the sauce. Spoon sauce over the fillets. Garnish with more basil and Parmesan, and serve immediately.