In a small mixing bowl, whisk together the brown sugar, paprika, garlic powder, onion powder, salt, black pepper, and chili powder until well combined.
Pat the salmon fillets dry with paper towels to ensure a proper sear.
Brush all sides of the fillets with olive oil, then generously coat the top and sides with the prepared seasoning rub, pressing it into the flesh.
Preheat a grill or heavy-bottomed skillet over medium-high heat (approximately 375°F to 400°F).
Place the salmon fillets on the cooking surface and sear for 4 to 5 minutes per side, or until the internal temperature reaches 145°F and the rub has formed a caramelized crust.
While the salmon cooks, combine the melted butter and lemon pepper seasoning in a small ramekin.
Remove the salmon from the heat and immediately brush the lemon pepper butter over the top of each fillet.
Serve immediately with lemon wedges on the side.