Combine the warm water, yeast and sugar in a small jug. Set aside for 5 minutes or until frothy.

Combine the flour, flour improver and salt in a large bowl and make a well in the centre. Pour yeast mixture into the well and stir until mixture just comes together. Turn onto a lightly floured surface and knead for 10 minutes or until dough is smooth and elastic. Place in a large bowl and loosely cover with plastic wrap. Set aside in a warm, draught-free place for 30 minutes or until dough rises by half.

Preheat oven to 180°C. Combine the 2 litres of water and sugar in a large saucepan over high heat; bring to the boil. Reduce heat to medium; bring to a simmer.

Brush an oven tray with oil. Divide the dough into 12-14 even portions. Roll each portion into a ball. Push a lightly floured finger through the middle of the ball to create a hole. Gently flatten the ball slightly. Place on the oiled tray and set aside for 10 minutes to rise slightly.

Add 4 of the bagels to the simmering water and cook for 3 minutes. Use a slotted spoon to turn and cook for a further 3 minutes. Use the slotted spoon to remove and transfer to oiled oven tray. Repeat in 2 more batches with remaining bagels.

Whisk the egg yolk and milk together in a small bowl. Brush evenly over each bagel and sprinkle with sesame seeds. Bake in preheated oven for 20 minutes or until golden brown and cooked through. Remove from oven and set aside to cool.