Place the shrimp and fish on a plate lined with paper towels and gently pat them dry on all sides. Removing excess moisture is important because it helps the seafood sear properly and prevents the sauce from becoming watery later.
Set a large skillet over medium heat and add the butter. Let it melt completely and start to gently bubble, but do not let it brown, as burnt butter can overpower the delicate seafood flavor.
Add the shrimp to the skillet in a single layer. Let them cook undisturbed for about 1–2 minutes per side, just until they turn pink and opaque. As soon as they are cooked through, transfer the shrimp to a plate and set aside to avoid overcooking.
Place the fish pieces into the same skillet. Lightly sear them for 1–2 minutes per side, just until the surface is lightly golden and the fish begins to flake. Remove the fish from the skillet and set it aside with the shrimp.
Lower the heat slightly and add the minced garlic to the skillet. Cook gently for about 20–30 seconds, stirring constantly, until the garlic becomes fragrant. Be careful not to let it brown, as garlic can turn bitter if overcooked.
Pour the chicken broth into the skillet, scraping the bottom gently with a spoon to loosen any flavorful bits. Add the heavy cream and bring the mixture to a gentle simmer, allowing it to cook for a few minutes until it begins to thicken slightly.
Stir in the parmesan cheese and lemon juice, mixing slowly until the cheese melts completely and the sauce becomes smooth and creamy. Taste the sauce and adjust seasoning if needed.
Return the shrimp and fish to the skillet, placing them gently into the sauce. Use a spoon to coat the seafood evenly, being careful not to break the delicate fish pieces.
Let everything cook together for just 1–2 minutes, only until the seafood is warmed through. Remove from the heat immediately and serve while hot, creamy, and perfectly tender.