In a small bowl, combine the softened butter, finely chopped fresh dill, and minced garlic, stirring until well blended. Set aside at room temperature so it stays spreadable. Pat the salmon fillets dry with paper towels and season both sides generously with kosher salt and freshly ground black pepper. Let the salmon sit at room temperature for 10-15 minutes while you prepare the grill—this allows it to cook more evenly and helps develop a better crust.

Preheat your grill to high heat for at least 10 minutes to ensure proper searing. While the grill heats, slice the large lemon into 1/4-inch rounds and set aside—these will create a flavorful bed for the salmon and prevent sticking. Once the grill is hot, use a grill brush to clean the grates thoroughly, then fold a paper towel, dip it in the olive oil, and carefully wipe down the grates. I find this oil-and-paper-towel method creates a better non-stick surface than spray oils and gives you more control.

Brush the salmon fillets lightly on both sides with the remaining olive oil. Place them skin-side down on the oiled grill grates directly over the high heat. Let them sear undisturbed for 2-4 minutes until the skin crisps and releases easily from the grill—you'll know it's ready when it doesn't stick when you try to move it. Avoid the temptation to move them around; this creates a beautiful golden crust and helps lock in moisture.

Carefully flip the salmon fillets using a fish spatula or wide metal spatula, then immediately lower the grill heat to medium. Place the lemon slices directly on the grill grates, arranging them in an area with medium heat. Cover the grill and cook the salmon for 3-5 minutes until it flakes easily with a fork and reaches an internal temperature of 145°F. The residual heat and gentle cooking will finish the fish while keeping it moist inside.

Transfer the salmon fillets to a serving platter, arranging 2-3 grilled lemon slices under each fillet. Top each salmon fillet with a generous dollop of the dill butter mixture from Step 1, allowing it to melt slightly over the warm fish. Serve immediately while the butter is still melting—the combination of the warm salmon, citrus, and herb butter creates an elegant, restaurant-quality dish that's ready in about 20 minutes.