In the bowl of a stand mixer (or a large mixing bowl), combine the warm water, yeast, and 1 tablespoon of sugar. Stir gently and let it sit for 5-10 minutes until foamy, indicating the yeast is active.

Add the bread flour and salt to the yeast mixture. Using the dough hook attachment (or a sturdy spoon), mix on low speed until a shaggy dough forms. Increase speed to medium-low and knead for 8-10 minutes, or until the dough is smooth, elastic, and pulls away from the sides of the bowl. If kneading by hand, knead on a lightly floured surface for 10-15 minutes.

Lightly grease a large clean bowl with olive oil. Place the dough in the bowl, turning once to coat. Cover the bowl with plastic wrap or a clean kitchen towel and let it rise in a warm place for 1.5 to 2 hours, or until doubled in size.

Gently punch down the risen dough to release the air. Turn it out onto a lightly floured surface. Flatten the dough into a rough rectangle. Sprinkle 1 cup of shredded cheddar cheese and all of the diced jalapeños evenly over the dough. Fold the dough over itself and knead lightly for 1-2 minutes to evenly distribute the fillings.

Divide the dough into 8 equal pieces (approximately 110-120 grams each). Roll each piece into a smooth ball. To shape each bagel, poke a hole in the center of a dough ball with your thumb and gently stretch the dough outwards to create a 1.5-2 inch hole. Ensure the hole remains open as the bagels will expand.

Place the shaped bagels on baking sheets lined with parchment paper, leaving some space between them. Cover loosely with plastic wrap or a kitchen towel and let them rest at room temperature for 20-30 minutes, or place in the refrigerator for 30 minutes to firm up.

Preheat your oven to 425°F (220°C). Prepare two baking sheets by lining them with parchment paper.

In a large pot, bring 8 cups of water to a rolling boil. Add the baking soda and honey to the boiling water. Reduce heat slightly to maintain a gentle boil.

Carefully place 2-3 bagels into the boiling water (do not overcrowd the pot). Boil for 30 seconds on each side. Using a slotted spoon or spider strainer, remove the bagels and place them back on the prepared parchment-lined baking sheets.

In a small bowl, whisk together the egg and 1 tablespoon of water to create an egg wash. Brush the top of each boiled bagel generously with the egg wash. Immediately sprinkle the remaining 1/2 cup of shredded cheddar cheese onto the tops of the bagels.

Bake in the preheated oven for 20-25 minutes, or until the bagels are golden brown and cooked through. If desired, rotate the baking sheets halfway through baking for even browning.

Remove from the oven and transfer the bagels to a wire rack to cool slightly. Serve warm with cream cheese, butter, or enjoy plain.