Stir the warm water, sugar, and active dry yeast together in a small bowl. Let it sit for 10 minutes until a thick, foamy head develops. This ensures your yeast is alive and ready to provide the high-protein dough with a professional-grade rise.
Combine the bread flour, salt, and yeast mixture in a large bowl. Stir in half a cup of shredded cheddar. Turn the dough onto a floured surface and knead for 10 minutes until smooth and elastic. The high protein in the bread flour is what creates that signature New York-style chew.
Place the dough in a lightly greased bowl, cover with a towel, and let it rise in a warm spot for 60 to 90 minutes. You want the dough to double in size, which allows the savory flavors to develop and the texture to lighten.
Punch down the dough and divide it into 8 equal portions. Roll each into a ball and poke a hole through the center with your thumb, stretching it to about two inches. This classic shape ensures even cooking during the boiling and baking stages.
Drop the bagels into a pot of boiling water mixed with honey or barley malt syrup. Boil for 1 minute per side. This essential step gelatinizes the starch on the surface, creating the shiny, chewy crust that defines a top-notch bagel.
Brush the boiled bagels with an egg wash and pile the remaining sharp cheddar on top. Bake at 425°F for 20 to 25 minutes until the cheese is bubbly and the crust is golden. Let them cool slightly so the internal crumb sets perfectly.
