Preheat the oven to 375 degrees F. Place parchment paper on a baking sheet. Lightly coat with cooking spray to prevent the bagels from sticking.
In a large bowl, use a sturdy spatula to combine the self-rising flour and yogurt until the mixture clumps to a shaggy dough. Dump the mixture onto a lightly floured work surface. Knead the dough together by hand for about 5 minutes, until the dough is smooth and elastic. Dust with additional flour as needed if the dough is too sticky (see Recipe Notes below for tips).
Divide the dough into 8 equal parts. Shape each portion of dough into a ball. Use your thumbs to make a hole in the center of each ball. Gently pull and stretch until the dough is a uniform sized ring. Repeat with remaining rounds. Flour your hands as needed.
Arrange the shaped bagels on the prepared baking sheet. Mix together the egg wash by whisking the egg, salt, and water in a small bowl until smooth. Brush the egg wash mixture over the bagels. Sprinkle desired toppings over bagels.
Bake for 20 to 22 minutes, rotating the baking sheet midway through baking. Remove from the oven. Increase oven temperature to 450 degrees F. Return the baking sheet to the oven and bake for another 3 to 4 minutes until the tops of the bagels have browned.
