Pat the salmon dry with paper towels. Season with salt and pepper to taste. Set aside.
Adjust the oven rack to the middle position. Preheat the broiler. In a small bowl, whisk together the garlic, brown sugar, bourbon, soy sauce, and green onions.
Add the butter and oil to a large, oven-safe skillet (at least 12 inches in diameter) over medium-high heat. Once the butter melts, whisk in the bourbon mixture. Bring to a boil over medium-high heat and cook, whisking constantly, for about 1-2 minutes. Add the salmon, skin side down (if using salmon with skin); cook for 3 minutes. Baste the salmon with the sauce by spooning the sauce over the salmon periodically as it cooks.
Transfer the skillet to the middle rack under the broiler. Broil the salmon for 5-6 minutes, basting with the bourbon glaze about halfway through, until the salmon is caramelized on top and the fish flakes easily with a fork.