Pat halibut dry, and then pat it dry again. Allow it to come to room temperature.
Meanwhile, pour balsamic vinegar and bourbon together and set aside. Keep the balsamic-bourbon mixture within arm's reach, so that you can grab it quickly when the honey is ready.
Pour honey into a small, heavy bottom pot and turn heat to medium. In about 1-2 minutes, the honey should start to bubble. Stir it with a wooden spoon until the honey darkens in color and turns amber (about 3 more minutes). The caramelizing honey will be EXTREMELY hot. Do not touch it or attempt to taste it at this point. Carefully, standing back from the pot in case of splash-back, pour the balsamic and bourbon mixture into the pot with the honey. Stir, and cook for 1-2 more minutes. Take sauce off the heat, and set aside. If the sauce cools and thickens too much while the fish is cooking, simply set it back on the heat for about a minute, or until it heats up again.
Heat 1 TB butter and all of the olive oil in a heavy-bottom pan over medium heat.
Salt both sides of the halibut.
Set halibut in hot pan, and DO NOT TOUCH IT. Sear for 3-4 minutes, or until you can flip the halibut with a thin metal spatula. If it sticks to the pan, wait another 30 seconds. The fish will release when it's done cooking.
Divide the remaining butter and set it on top of the two halibut fillets, allowing it to melt as the fish cooks. Sear them for 3-4 more minutes, and then remove halibut from the pan. Set fish to the side, and cover to keep warm.
Lower heat to medium. Add fresh spinach to the hot pan, and toss for about 30 seconds, or until it begins to wilt. Transfer spinach to plates, and top with the fish.
Serve spinach and fish immediately with bourbon dressing.