Place the butter and pesto in a small bowl and beat until combined. Place a foot long sheet of plastic wrap on a work surface; spoon on the butter. Roll the butter inside the plastic wrap into in a 1 1/2" thick log. Refrigerate the butter until firmed up, about 2 hours. Preheat your barbecue or indoor grill to medium-high. Brush and lightly coat each salmon steak with the 1 Tbsp. oil. Season the steaks with salt and pepper. Slice the butter into 8 to 12 rounds and set on a plastic-wrap-lined plate.
Lightly oil the bars of the grill. Grill the salmon 3 to 4 minutes per side, or until just cooked through. Set the fish on plates, top each with 2 to 3 rounds of the butter, and serve.