Add the water and flour to the bowl of a stand mixer fitted with a dough hook, and mix for 2 minutes. Let rest for 20 minutes.
Add the pâte fermentée, yeast, and salt and mix on low speed until the dry ingredients are completely combined. Add a little more water if this hasn’t happened in 3 minutes. Increase the speed to medium to medium-high and mix until the dough is smooth, pulls away from the sides of the bowl and leaves the sides clean, has a bit of shine, and makes a slapping noise against the sides of the bowl, 5 to 7 minutes. Do the windowpane test to check to see if the gluten is fully developed.
Cover the bowl with plastic wrap or a plastic bag and let stand at room temperature until doubled in volume.
Transfer the dough to a lightly floured surface. Divide the dough into 12 equal pieces (each weighing about 80 g). Form each piece into a small bun, cover with clingfilm, and let rest for 5 minutes. Press each ball into a flatter disk of dough.
Line 2 baking trays with parchment or a silpat. Place the disks of dough, evenly spaced on the baking trays. Loosely cover with clingfilm or a tea towel. Let them rest for an hour or so.
Preheat the oven to 350C
Uncover the bialys and, using the pads of your fingers, make a depression in the center of each disk of dough. Put a teaspoon of the poppy/onion filling in the centre of each bialy.
Bake for 12 to 15 minutes or until golden. Transfer to a wire rack to cool for a few minutes.
Serve immediately. You can also freeze these for later use.