The trick to these crisp, chewy bagels is the poolish, a fermentation starter (also known as a mother dough) made with bread flour, yeast and water. It is quickly assembled the night before the bagels are made. Slideshow: Bagel Toppings
In a medium bowl, using a wooden spoon, stir the bread flour with the yeast and 1 cup of lukewarm water until combined. Cover with plastic wrap and refrigerate overnight.
In the bowl of a standing mixer fitted with the dough hook, combine the yeast and honey with 1 2/3 cups of lukewarm water. Mix in the poolish. Add the bread flour, whole wheat flour and salt and beat at medium speed until a smooth, stiff dough forms, 5 to 7 minutes. Transfer the dough to a lightly floured work surface and knead for 1 minute. Form the dough into a ball and transfer to a large, oiled bowl. Cover with plastic wrap and let stand in a draft-free spot until doubled in volume, about 1 hour.
Line a baking sheet with parchment paper and brush or spray generously with vegetable oil. Divide the dough into 12 pieces and form into tight balls; transfer to the baking sheet. Cover loosely with sprayed plastic wrap and let stand for 30 minutes.
To form the bagels, poke your finger in the center of each ball to make a 1/2-inch hole. Return the bagels to the baking sheet, cover and let stand until risen, about 1 hour. Add 1 bagel to a bowl of cold water. If it floats, the bagels have risen sufficiently.
Preheat the oven to 475° and position racks in the lower and middle thirds. Line 1 baking sheet with a clean, lightly moistened kitchen towel and line 2 others with parchment paper; spray the paper with oil. Bring 2 large, deep pots of water to a boil. Add 1/2 tablespoon of baking soda to each pot. Add 2 or 3 bagels to each pot, without crowding (the bagels will swell in the water) and simmer for 1 1/2 minutes. Flip the bagels and simmer for 1 1/2 minutes longer. Using a slotted spoon, transfer the bagels to the kitchen towel–lined sheet to drain. Before they dry, sprinkle the bagels generously with toppings, then immediately transfer them to the parchment paper-lined baking sheets. Repeat with the remaining bagels.
Bake the bagels for 18 to 20 minutes, shifting the pans from top to bottom and front to back halfway through, until deeply browned. Let cool slightly, then serve.
The bagels can be stored in an airtight container for up to 3 days. Sprinkle with water and reheat in a 350° oven until crusty and warm.