Grease 2 large bowls with 1 teaspoon of oil each. Set aside.
Combine the water, yeast and 3 tablespoons of the sugar in the bowl of a stand mixer fitted with a dough hook. Stir and let stand until foamy, about 5 minutes.
Turn the mixer to low speed, gradually add 4 cups of the flour and the salt and mix until a sticky dough forms. Turn off the mixer and use a wooden spoon or your hands to mix in the remaining 2 cups flour, 1/2 cup at a time, until a stiff dough forms. (The dough will seem dry with too much flour, but it will be perfect once it's kneaded.)
Turn out onto a lightly floured surface and divide in half. Cover one portion of dough with a clean towel. Knead the other portion of dough until smooth and no longer sticky, adding just as much flour as needed, about 5 minutes. (The dough should be heavier and stiffer than regular yeast bread dough.) Put the dough in one of the prepared bowls, turning to coat with oil. Cover with plastic.
Add the red food coloring to the second portion of dough and knead until smooth and no longer sticky, adding just as much flour as needed, about 5 minutes. Put the dough in the other prepared bowl, turning to coat. Cover with plastic. Let the dough rise in a warm, draft-free spot until almost doubled, about 1 hour.
Grease 2 baking sheets with the remaining 1 tablespoon oil.
Punch the plain dough down in the bowl and remove to a work surface. Divide into 12 pieces, about 2 ounces (55 grams) each. Cover with a clean towel. Repeat with the red dough.
Roll each portion of plain dough into a ball, then roll into a 10-inch log. Repeat with the red dough. Twist one plain log and one red log together to look like a striped peppermint stick. Join the ends, placing your fingers through the hole, then roll the ends together. Transfer to the prepared baking sheets and cover with a clean cloth while you shape the rest. Let rest in a warm, draft-free spot until risen but not doubled, 20 to 30 minutes.
Meanwhile, preheat the oven to 400 degrees F and sprinkle the cornmeal onto 2 baking sheets.
In a large, heavy pot, bring 12 cups of water and the remaining 1 tablespoon sugar to a boil. In batches of 2, add the bagels to the water and boil, flipping halfway through, until the bagels expand slightly, 1 minute. Transfer the bagels to the prepared baking sheets with a slotted spoon. Bake until golden, 30 to 35 minutes. Let cool on a wire rack.
When measuring flour, we spoon it into a dry measuring cup and level off excess. (Scooping directly from the bag compacts the flour, resulting in dry baked goods.)
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