Preheat oven to 375 degrees Fahrenheit and line a baking sheet with parchment paper.
In a medium bowl, combine the self-rising flour and Greek yogurt using a spatula until a thick dough forms.
Transfer the dough to a lightly floured surface and knead gently for 2 minutes until smooth and no longer sticky.
Divide the dough into 4 equal portions.
Roll each portion into a rope approximately 6 inches long and join the ends to form a ring.
Place the bagels on the prepared baking sheet and brush the tops with the beaten egg.
Sprinkle with everything bagel seasoning.
Bake for 22 to 25 minutes until golden brown.
Allow to cool for 15 minutes before slicing to ensure the interior set.