Combine all the ingredients for the pâte fermentée in a mixing bowl. Mix until a shaggy dough forms; cover with a plastic wrap and let stand at room temperature for 30 minutes.

Refrigerate the mixture for at least 8 hours and up to 24 hours.

Combine the water and flour in a mixing bowl or the bowl of a stand mixer. Let it rest for 20 minutes.

Next add the pâte fermentée (straight from the fridge -- no need to bring to room temperature), yeast and salt -- mix until all the ingredients are well combined. Add a little more water if needed to make a smooth, pliable dough. Knead for 7 (on mixer) ~ 10 minutes (by hand).

Transfer the dough to a clean bowl. Cover and set aside for about 1½hours or until doubled in volume.

Heat oil in a large skillet on medium-low heat. Add the onions and cook, stirring occasionally, until the onions just start to brown and have reduced in volume, about 15~20 minutes.

Transfer the onions to a bowl and stir in the bread crumbs, poppy seeds and salt. Set aside to cool.

Transfer the dough to a lightly floured surface. Divide the dough into 12 equal pieces. Form each piece into a small bun; cover with plastic wrap and let rest for 5 minutes.

Once all the pieces have turned into buns, proceed in the same order in which the pieces were shaped into balls; flatten each ball with the heel of your hand into a disk about 2" diameter.

Place the disks on the back of a baking sheet that is lined with parchment paper. Loosely cover with plastic wrap and set aside for 1~1½hours.

Preheat the oven to 500°F for at least 30 minutes.

Uncover the bialys and using the index and middle fingertips make a depression in the center of each disk of dough. Put about 1tbsp of the filling and a tiny bit of cheese on each bialy.

Bake until golden brown, about 12~15 minutes. Transfer to a wire rack to cool for a few minutes. Serve right away. Leftovers can be kept in an airtight container at room temperature for up to 2 days.