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Cut the onions into thin wedges, keeping the root intact so they hold together, to make about 12-16 thin wedges.
Whisk the eggs and flour in a large bowl to make a smooth paste, then whisk in the milk to make a smooth batter. Season, then stir in the sage. Leave to rest for 10 mins at room temperature. Will keep chilled for up to 24 hrs (bring up to room temperature before using). Heat the oven to 230C/210C fan/gas 8.
Pour a drizzle of oil evenly into 10 holes of a 12-hole muffin tin, or in all of two four-hole Yorkshire pudding tins to coat the bases. Add a wedge of onion to each hole and put in the oven for 10 mins to heat up.
Transfer the batter to a jug, carefully remove the tins from the oven and pour the batter over the onions, dividing it evenly between the holes. The batter should sizzle as soon as it hits the oil. Put back in the oven and turn the temperature down to 220C/200C fan/gas 7. Cook for 15 mins until golden and risen. Don’t open the door until the time is up, or they may sink.