In a mixing bowl, combine warm water with granulated sugar. Stir gently until the sugar dissolves, then sprinkle in the active dry yeast. Let sit for about 10 minutes until frothy.

Add eggs and vegetable oil to the yeast mixture, whisking until well combined. Gradually mix in bread flour and salt until a soft dough forms. Knead on a floured surface for about 10 minutes.

Place dough in a lightly oiled bowl, cover, and set in a warm area to rise for 1 to 1.5 hours, until doubled in size.

Gently punch down the dough, divide it into 12 pieces, and shape each into a bagel, maintaining even thickness.

Boil water with sugar in a large pot. Add bagels, boiling 4 at a time for 1 minute on each side. Transfer to a parchment-lined baking sheet.

Preheat the oven to 400°F. Brush boiled bagels with egg wash and sprinkle with cheddar cheese. Bake for 20 to 25 minutes until golden.

Remove bagels from the oven and let cool on a wire rack for about 10 minutes before serving.