For poolish, combine flour, yeast and 50ml water in a small bowl. Cover and refrigerate overnight.

For dough, combine flour, sugar, yeast and poolish in the bowl of an electric mixer fitted with a dough hook. Gradually incorporate oil and 340ml water on low speed, alternating oil and water, until dough comes together (2-2½ minutes). Turn out onto a lightly floured surface and knead until a smooth dough forms (about 5 minutes). Add 1 tsp salt and knead until combined. Form into a ball and place in an oiled bowl, then cover and set aside to prove in a warm place until doubled in size (1½ hours). Divide dough into 24 balls, then set aside on a lightly oiled tray to prove again until light and aerated (20 minutes).

Meanwhile, for bagna cauda, blend anchovies, garlic, lemon zest and juice and milk with a hand-held blender until smooth, then gradually add oil in a thin, steady stream and blend until mixture is thick and emulsified.

Preheat oil in a large saucepan to 180°C. Roll out dough balls one at a time on a lightly floured surface until 2mm thick. Deep-fry, in batches, carefully spooning oil over so dough puffs up (2-3 minutes; be careful, hot oil will spit). Remove with a slotted spoon and place on a tray lined with paper towel.

To serve, spoon a generous amount of bagna cauda onto each pizza fritta and top with grated Parmigiano-Reggiano.