Whisk 240g of lukewarm water, 2 tablespoons of sugar, and 15g of active dry yeast. Leave for 5 minutes.
Beat in 240g of lukewarm milk, 450g of all-purpose flour, 1 level teaspoon of salt, and 4 tablespoons of olive oil for about 2 minutes, until smooth.
Cover and leave in a warm place for at least 1 hour, until risen and bubbly.
Heat a deep pan of vegetable oil to 320°F / 160°C. Use two lightly oiled spoons to drop small spoonfuls of batter close to the oil surface, without crowding.
Fry, turning with a slotted spoon, until golden on every side and cooked through. Drain on paper towels and repeat with the remaining batter.
Drizzle the warm doughnuts with ¾ cup of honey. Sprinkle with ground cinnamon and chopped walnuts, then serve immediately.