Use paper towels to pat the halibut fillets completely dry - this will ensure even browning. Season the fish on both sides with garlic powder, paprika, sea salt, and black pepper. Set aside.
Heat the olive oil in a large skillet over medium-high heat for 2 minutes.
Add the fish fillets in a single layer (you can do it in batches if all the fish won't fit in a single layer). Sear, without moving, for 3-4 minutes, until the edges of the fish are opaque. Flip and cook for 2-4 minutes, until cooked through.
Remove the fish from the pan and cover tightly with foil to keep warm.
Reduce heat to medium-low. Add the butter to the same pan. Wait for it to melt, then heat for 2-3 minutes, stirring occasionally, until the butter is browned and smells nutty.
Use a lemon squeezer to squeeze all the juice from both halves of the lemon into the pan. Bring to a simmer, then reduce heat and simmer for about 3-4 minutes, stirring often, until volume is reduced by half. The lemon butter sauce will still be thin.
Drizzle a little lemon butter sauce over each serving plate. Place the pan seared halibut fillets over the sauce, then drizzle more sauce on top.