Preheat the pellet grill to 350°F using a mild pellet.
Pat the salmon dry with paper towels and check for and remove pin bones. Place it skin-side down on a sheet pan, or if it is skinless, place it on a parchment-lined sheet pan. Brush salmon with olive oil.
Season it evenly with kosher salt and black pepper.
Stir the softened butter, garlic, dill, parsley, lemon zest, lemon juice, and kosher salt together until evenly combined.
Place dollops of the compound butter over the salmon fillet.
Spread the compound butter over the top of the salmon in an even layer.
Place the salmon skin-side down on the pellet grill. If you are using parchment paper, place the parchment paper directly on the grill grates. Close the lid and cook without flipping until the thickest part reaches 120°F to 125°F internal temperature, about 18 to 25 minutes depending on thickness.
Remove the salmon from the grill and rest for 5 minutes. Serve with lemon wedges.