Make the filling
Heat the olive oil in a medium skillet over medium heat. Add the onion, poppy seeds, salt, and black pepper. Cook, stirring occasionally, until the onion is translucent but hasn’t yet started to color, 5 to 7 minutes. Set aside to cool completely.
Make the dough
Pour the water into the bowl of a standing mixer. Add the yeast, flour, and salt and stir with a rubber spatula just until all the water is absorbed and a rough dough forms. Attach the dough hook and knead the dough on medium speed until it is springy and smooth, 5 to 6 minutes.
Transfer the dough to a lightly oiled bowl or dough-rising container, cover the bowl with plastic wrap, and let stand at room temperature until it has doubled in volume, about 2 hours.
Line a baker’s peel or a rimless baking sheet with parchment paper. Set another piece of parchment paper on the counter.
Turn the dough out onto the parchment paper on the counter and use a bench scraper or sharp chef’s knife to divide it into 10 equal pieces. Shape each piece into a tight round.
Transfer half of the rounds, seam sides down, to the lined peel or baking sheet, leaving at least 2 inches between each one. Transfer the other half to the other piece of parchment paper. Lightly dust with flour, drape with plastic wrap, and let stand until increased in size about 1-1⁄2 times, about 1-1⁄2 hours.
One hour before baking, place a baking stone on the middle rack of the oven. Heat the oven to 450°F.
Press both thumbs into the center of each bialy, creating a shallow well. Don’t make the center too thin—think about making a mini pizza. Pierce the wells with the tines of a fork to prevent them from bubbling up in the oven. When all of the bialys are shaped, fill each one with a heaping teaspoon of the filling.
Slide the first batch of bialys, the ones on the peel or baking sheet, onto the baking stone. Bake until golden brown, 7 to 9 minutes.
Slide the peel or the rimless baking sheet under the parchment paper to remove the bialys from the oven. Cool for about 5 minutes on a wire rack, and then peel them off the parchment paper. Repeat with the second batch of bialys, sliding them, still on the parchment, onto the peel or baking sheet, and then sliding them, still on the parchment, onto the baking stone. Bialys are best eaten on the day they are baked. For longer storage, freeze in a zipper-lock plastic bag for up to 1 month. To defrost, place on the countertop for 15 to 30 minutes, and reheat in the oven at 350°F for 5 minutes before serving.