1. To make the batter, sprinkle the yeast over the warm water in a medium bowl. Let stand for 5 minutes. Stir to dissolve the yeast. Stir in the milk and sugar. Add the flour and whisk until smooth. Cover with a towel and let stand in a warm place until bubbling, about 1 hour.

2. Peel the potatoes and cut into sticks about 2½ in (6cm) long and ½ in (1cm) wide. Rinse, drain, and pat dry with paper towels.

3. Preheat the oven to 250°F (130°C). Fill a wide, deep saucepan halfway with oil and heat to 325°F (160°C). Place half the potatoes in a deep-frying basket and lower carefully into the hot oil. Deep-fry for 5 minutes, or until the potatoes are tender but pale-colored. Drain and transfer to a baking sheet. Repeat with the remaining potatoes.

4. Line another baking sheet with paper towels. Season the cod with salt and pepper and dust with flour. Increase the oil temperature to 375°F (190°C). In two batches, dip the cod in the batter, carefully add to the oil, and deep-fry until golden brown. Transfer to the sheet and keep warm in the oven.

5. Return all the potatoes to the frying basket and deep-fry for 3–4 minutes, shaking the basket occasionally. Drain well. Serve hot, garnished with parsley and lemon.