1) Place the dough ingredients in a bowl, and mix and knead — by hand, mixer, or bread machine — for about 7 minutes, till you've made a smooth, fairly stiff dough.
2) Place the dough in a lightly greased bowl or other rising container, cover it, and allow it to rise for about 90 minutes, till it's just about doubled in bulk.
3) While the dough is rising, make the filling. Fry the diced onion in the oil over high heat; it'll brown very quickly, so stir often. Fry till it's a dark golden brown, with even darker charred bits. Sprinkle with the salt, stir to combine, and remove from the heat. Transfer to a small bowl to cool.
4) Preheat the oven to 450°F.
5) Gently deflate the dough, and divide it into 8 pieces. Shape four of the pieces into 4" to 5" circles, each with a small rim. (Keep the remaining pieces of dough covered.)
6) Place the shaped circles on a parchment-lined or lightly greased baking sheet.
7) Use a sharp knife or pair of scissors to snip a 1" hole in the bottom of each bialy.
8) Evenly spread the filling into the center of each bialy, the part defined by the rimmed edge.
9) Top the bialys with a sheet of parchment or aluminum foil; then with another baking sheet. You want to weigh them down.
10) Bake the bialys for 4 minutes. Remove them from the oven, and remove the baking sheet and parchment or foil.
11) Return the bialys to the oven, and bake for an additional 7 minutes, till they're a dappled golden brown.
12) Remove from the oven, and cool on a rack. Repeat with the remaining dough.
Yield: 8 large bialys.