In a large bowl, cover the potatoes with water; let soak for 1 hour. Drain the potatoes and pat dry thoroughly with paper towels.
Set a rack over a rimmed baking sheet. In a large, wide pot, heat 2 inches of oil to 330°. Add the potatoes and fry until tender, about 12 minutes. Using a long-handled wire scoop, transfer the potatoes to the rack to drain. Let cool for at least 15 minutes.
Meanwhile, in a large bowl, whisk the 1 1/2 cups of flour with 1 1/2 teaspoons of salt. Whisk in 1 1/2 cups of the cold beer until the batter is almost smooth; it should be a little lumpy. Refrigerate for 15 minutes. Stir in the remaining 1/4 cup of beer.
Preheat the oven to 350° and heat the oil to 375°. Add half of the potatoes and fry until crisp, 2 minutes; transfer to the rack to drain while you fry the remaining potatoes. Spread the fries on a large rimmed baking sheet.
Reduce the oil temperature to 325°. Season the fish with salt and pepper. Mound flour in a wide, shallow bowl. Working with 2 pieces at a time, dredge the fish in the flour, shaking off the excess. Dip the floured fish in the beer batter; allow any excess batter to drip off. Add the battered fish to the hot oil and fry, turning a few times, until richly browned and crunchy and the fish is cooked through, 8 to 10 minutes. Drain the fish on the rack, lightly blot dry with paper towels and keep warm.
Reheat the fries in the oven. Batter and fry the remaining fish. Serve the fish and chips hot with malt vinegar and Dilled Tartar Sauce.