In a bowl, combine the sourdough starter pieces with the sugar, olive oil, and water. Stir until the starter dissolves, then add the flour and start mixing.

When the dough begins to come together, add the salt. Knead until the dough pulls away from the sides of the bowl.

Transfer the dough to a floured work surface and roll it out with a rolling pin. Fold the right side toward the center, then fold the left side toward the center to form a dough ball.

Roll out the dough again and repeat the folding process. Once you have a dough ball again, place it in an oiled bowl and brush the top with a little more olive oil. Cover with plastic wrap and let rise in a draft-free place until doubled in size, about 3 to 4 hours.

Return the dough to the floured work surface and roll it out with a rolling pin. Cut into squares and place them on a baking sheet lined with parchment paper.

Remove the plastic wrap and use your fingertips to make dimples in the dough. Brush the tops with the prepared emulsion.

Bake at 375°F (190°C) for about 15 minutes. Let cool slightly before cutting, as they will be hot and crispy.