In a large bowl, whisk together the flour, baking powder, salt, and black pepper. Gradually add the cold beer, stirring until the batter is smooth and well combined. Let the batter rest for about 10 minutes.

While the batter rests, heat about 2 inches of vegetable oil in a deep skillet or pot over medium-high heat until it reaches 350°F.

Dip each piece of halibut into the batter, allowing any excess to drip off. Carefully place the battered fish into the hot oil, working in batches to avoid overcrowding.

Fry the halibut for about 4-5 minutes, turning occasionally, until golden brown and cooked through. Use a slotted spoon to transfer the fish to a paper towel-lined plate to drain excess oil.

Serve the crispy beer-battered halibut hot with lemon wedges and tartar sauce on the side.