Combine water, blueberries, yeast and 30 grams of caster sugar in a jug. Set aside for 5 minutes or until frothy.
Combine the flour, cinnamon and salt in a large bowl and make a well in the center. Pour the 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 250°F. Combine extra water and remaining caster sugar in a large saucepan over high heat and bring to the boil. Reduce heat to medium and bring to a simmer.
Brush an oven tray with oil. Divide dough into eight even portions. Roll each portion into a ball. Push a lightly floured finger through middle of ball to create a hole. Flatten ball slightly. Place on oiled tray and set aside for 10 minutes to rise slightly.
Add 4 of the bagels to simmering water; cook for 3 minutes. Use a slotted spoon to turn; cook for a further 3 minutes. Use a slotted spoon to remove and return to oiled tray. Repeat with remaining bagels.
Whisk egg yolk and milk together in a bowl. Brush evenly over each bagel; sprinkle with sugar. Bake in preheated oven for 20 minutes or until golden brown and cooked through. Remove from oven and set aside to cool. Serve toasted with cream cheese and berries, if desired.