1) To make the starter: Combine the ingredients in a medium-sized bowl, cover, and let rest at room temperature overnight.
2) To make the dough: Combine the puffy starter with all the dough ingredients, and knead — by hand, electric mixer, or bread machine — to form a stiff but not dry dough. Since we're using a high-protein bread flour here, you might notice it takes a bit more effort and time to develop the gluten.
3) Place the dough in a lightly greased bowl or large (at least 8-cup) measuring cup, cover, and set it aside to rise for 1 hour. Gently deflate the dough, and let it rise for another 30 minutes.
3) While the dough is rising, prepare the water bath by heating the water, baking soda, and malt powder or sugar to a very gentle boil in a wide-diameter (about 10") pan. A 10" electric frying pan works well here. Boil until the baking soda has dissolved, then turn off the heat.
4) Gently deflate the risen dough, transfer it to a work surface, and divide it into 12 pieces. Roll each piece into a smooth, round ball. Cover the balls with plastic wrap, and let them rest for 30 minutes. They'll puff up very slightly.
5) Preheat your oven to 425°F. Bring the water in the pan back to a simmer/slow boil.
6) Use your index finger to poke a hole through the center of each ball, then twirl the dough on your finger to stretch the hole until it's about 2" in diameter (the entire bagel will be about 3 1/2" across). Place each bagel on a lightly greased or parchment-lined baking sheet, and repeat with the remaining pieces of dough.
7) Transfer the bagels, four at a time if possible, to the simmering water. Increase the heat under the pan to bring the water back up to a gently simmering boil, if necessary. Cook the bagels for 2 minutes, flip them over, and cook 1 minute more. Using a skimmer or strainer, or the end of a wooden spoon, remove the bagels from the water and place them back on the baking sheet. Top each wet bagel with some of the shredded cheese. Repeat with the remaining bagels.
8) Bake the bagels for about 25 minutes, or until they're as deep brown as you like.
9) Remove the bagels from the oven, and cool completely on a rack.
Yield: 12 bagels.