Soak the cut potatoes in cold water for 20 minutes, drain, and dry thoroughly.
Heat the oven to 450 F. Toss the potatoes with a little oil and salt, spread them on a sheet pan, and bake for 30 to 35 minutes, turning once, until golden and crisp.
Make the Batter and Fry:
Whisk 1 cup of flour with the cornstarch, baking powder, half of the salt, and pepper. Whisk in the cold lager just until smooth.
Heat 2 inches of frying oil to 350 F in a deep heavy pot. Dust the fish with the remaining flour, dip into the batter, and let the excess drip off.
Fry the fish in small batches for 5 to 7 minutes, turning once, until deeply golden and cooked through. Drain on a wire rack and season with the remaining salt.
Make the Peas and Serve:
Warm the peas with the butter and lemon juice, then mash lightly with a fork.
Serve the fish with the hot chips, mushy peas, tartar sauce, and lemon wedges.
Notes
Keep the batter cold and mix it shortly before frying.
A wire rack keeps the fried fish crisp while the remaining pieces cook.
Use haddock or pollock in place of cod if preferred.