Set your oven rack to the center position and the other about six inches below the broiler, then preheat the oven to 375°F. Line a baking sheet lengthwise with a large piece of foil, making sure it's big enough to fold over the salmon, and lightly brush the foil with olive oil.

Grate the zest from one lemon into a small bowl, squeeze the juice from both lemons, then whisk them together with the olive oil, chopped garlic, oregano, paprika, and black pepper until well mixed.

Pat the salmon dry with paper towels, season both sides thoroughly with kosher salt, then place it skin-side down on the prepared foil. Pour the lemon garlic sauce evenly over the top, lifting the foil edges to hold in the sauce. Use a spoon or brush to spread it across the fish surface. Slice half of the remaining lemon into thin rounds and arrange them on top of the salmon.

Fold the foil loosely over the fish, creating a tent with some air space around the lemon slices. Seal the edges of the foil tightly, crimping to enclose the salmon and trap steam inside. If necessary, use an additional foil piece to fully wrap the fish.

Bake the wrapped salmon in the preheated oven until it is nearly cooked through in the thickest area, about 15 to 20 minutes depending on thickness.

Carefully open the foil to expose the top of the salmon, then switch your oven to the broiler setting on high. Place the salmon under the broiler for about 3 minutes until it browns lightly and finishes cooking. Keep an eye on it to avoid burning the garlic or lemon.

Remove the salmon from the oven, sprinkle chopped parsley over the top, and serve immediately with the reserved lemon wedges on the side.