Step 1: Prepare the Salmon
Pat the salmon fillets completely dry with paper towels. This is crucial for getting a good sear. Season both sides generously with salt, black pepper, and paprika. Let the salmon sit at room temperature for 5-10 minutes while you prepare other ingredients.

Step 2: Sear the Salmon
Heat olive oil and 1 tablespoon of butter in a large skillet over medium-high heat until the butter melts and begins to shimmer. Place salmon fillets in the pan skin-side up (if using skin-on salmon) and sear for 4-5 minutes without moving them. The salmon should develop a beautiful golden-brown crust. Carefully flip using a fish spatula and cook for another 3-4 minutes until the salmon is cooked through but still slightly translucent in the very center. Transfer salmon to a plate and tent loosely with foil to keep warm.

Step 3: Make the Aromatic Base
Reduce heat to medium and add the remaining tablespoon of butter to the same skillet. Add minced garlic and sauté for 30-45 seconds until fragrant but not browned. Be careful not to burn the garlic as it will become bitter.

Step 4: Deglaze with Wine
Pour in the white wine and use a wooden spoon to scrape up any browned bits from the bottom of the pan (this is where tons of flavor lives!). Let the wine simmer for 2-3 minutes until reduced by about half.

Step 5: Create the Cream Sauce
Pour in the heavy cream and chicken broth, stirring to combine. Add the lemon juice, lemon zest, salt, and pepper. Bring the mixture to a gentle simmer and let it cook for 3-4 minutes, stirring occasionally, until it begins to thicken slightly.

Step 6: Add Cheese and Finish
Reduce heat to low and whisk in the freshly grated Parmesan cheese until melted and smooth. Stir in the chopped fresh parsley. Taste and adjust seasoning with additional salt, pepper, or lemon juice if needed. The sauce should coat the back of a spoon nicely.

Step 7: Combine and Serve
Return the salmon fillets to the skillet, nestling them into the creamy sauce. Spoon sauce over the top of each fillet. Let everything warm together for 1-2 minutes. Garnish with additional fresh parsley and lemon slices if desired. Serve immediately while hot.