In a mixing bowl, combine granulated sugar with warm water. Sprinkle the active dry yeast on top of the water and allow it to sit undisturbed for about 10 minutes, or until it becomes frothy.

Once your yeast is frothy, stir in the large eggs, vegetable oil, and salt until well combined. Gradually add in the bread flour, mixing until the dough comes together.

Transfer the mixture to a floured surface and knead for approximately 10 minutes, or until the dough is smooth and elastic.

Place the kneaded dough in a lightly oiled bowl, cover and allow it to rise in a warm spot for 1 to 1.5 hours, or until it has doubled in size.

Once the dough has risen, gently punch it down to release any air bubbles. Divide the dough into 12 equal pieces, shaping each piece into a smooth ball.

In a large pot, bring water to a boil and add a bit of sugar. Carefully add the bagels to the boiling water, cooking 4 at a time for 1 minute on each side.

After boiling, use a slotted spoon to remove the bagels and let them cool on a wire rack. Brush each bagel with egg wash and sprinkle with cheddar cheese or toppings.

Preheat your oven to 400°F and bake the bagels for 20 to 25 minutes, until golden brown.

Once baked, remove the bagels from the oven and transfer them to a wire rack to cool completely.