Mix flour and Greek yogurt together in a medium bowl until a shaggy dough forms. Transfer to a surface dusted with self-rising flour, and knead for 8 to 10 minutes. Continue adding flour as needed if the dough is too sticky.

Preheat the oven to 375 degrees F (190 degrees C).

Cut the dough into 4 pieces, roughly 4 ounces each. Roll each segment into a smooth ball. Use your thumbs to poke a hole in the center of each round, then gently stretch the dough until it becomes a uniform-sized ring.

Transfer the dough to a parchment paper-lined baking sheet.

Whisk the egg in a small bowl to create an egg wash, then brush a light coating on top of the dough. Sprinkle with bagel seasoning.