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Mix the water, yeast and sugar together, leave to rest for 5 mins. Mix the flour, yeast mixture, olive oil and eggs together. Add the salt without allowing it to touch the yeast directly. Mix together until it forms a ball.
Knead the dough and place it in a bowl brushed with 1 teaspoon of oil. Cover with a tea towel. Leave to rise for 30 mins until the dough has doubled in volume. Knead the dough once again.
Shape into a ball. Divide it into equal pieces the size of a walnut and roll into a sausage. Bring the two ends together. Set aside to rest for 10 mins. Boil 2L of water, plunge the bagels into boiling water 4 at a time for 1 to 3 minutes, turning them over in the water. Drain them, sprinkle them with poppy seeds or sesame seeds and salt.
Preheat the appliance, then bake the bagels for 5-7 minutes.