Pour ½ cup/120 milliliters lukewarm water into a small bowl. Whisk in 2 tablespoons barley malt syrup and the packet of yeast until both dissolve. Let sit until the mixture foams, about 5 minutes.

In a large bowl, combine bread flour and salt (and whole-wheat flour, if using), and make a well in the center. Pour in yeast mixture and the remaining 1¾ cups/420 milliliters lukewarm water, and mix, using the flexible spatula or wooden spoon, until the dough is shaggy.

Knead the mixture in the bowl several times, continuously folding it over and onto itself and pressing down firmly to bring it together in a solid mass, then turn it out onto a clean work surface. Continue kneading until there are no dry spots, then, adding more flour only if needed to prevent stubborn sticking, until you have a stiff but very smooth dough that is still slightly tacky, 15 to 20 minutes.

Gather the dough into a ball, dust it lightly with flour, and place it in a large, clean bowl, seam-side down. Cover with a damp towel and let the dough rise at room temperature until it has doubled in size, 1½ to 2 hours.

Using your fist, lightly punch down the dough to knock out some of the air, and turn it out onto a clean work surface. Using a bench scraper, cut the dough into 12 equal pieces.

Before you form the bagels, preshape the pieces into tight balls. Working one ball at a time, gather all the irregular edges and pinch them together firmly to make a teardrop shape. Place the dough seam-side down on the surface and cup your hand down and over top of the dough in a loose grip.

Line two large rimmed baking sheets with parchment paper, brush lightly with oil, and set aside. Working one piece at a time, roll out a ball on the surface beneath your palms into a 9-inch-long rope. Apply extra pressure at the ends of the rope to thin them slightly, then wrap the rope around one hand where your palm and fingers meet.

When you’ve formed all the bagels, cover each baking sheet with a piece of plastic, followed by a damp towel to create a sealed, moist environment for the bagels to proof slowly. Transfer the baking sheets to the refrigerator and chill at least 4 hours and up to 24.

About 2 hours before you’d like to serve the bagels, arrange an oven rack in the center position and heat the oven to 450 degrees. Fill a large, wide Dutch oven halfway with water and place it on the stove.

Remove one baking sheet from the refrigerator. Fill a small bowl with room temperature water, then carefully peel one ring of dough off the parchment paper and transfer it to the bowl. It should float, indicating that the bagels are ready to boil and bake.

Set the Dutch oven over high heat and bring to a boil. Whisk in the baking soda and ¼ cup barley malt syrup. You want the water to look like strong black tea, so add more barley malt syrup by the tablespoon until it does.

Use a spider or slotted spoon to transfer the bagels to the wire rack and repeat with the remaining bagels on the first sheet. The bagels will swell in the water, then deflate when removed, but they will puff up again in the oven.

Add the optional topping: Working with one at a time, place a boiled bagel on one of the plates with the toppings and turn to coat so the topping adheres to the wet surface of the dough on both sides.

Transfer the baking sheet to the oven and bake until the bagels are deeply brown, 20 to 25 minutes, rotating the baking sheet 180 degrees after 12 minutes.

Let the bagels cool completely on a wire rack before slicing with a serrated knife.