Preheat the oven to 350°F (175°C). Line a baking sheet with parchment paper.
In a medium mixing bowl, combine the self-rising flour and Greek yogurt until a sticky dough forms.
Transfer the dough to a lightly floured surface.
Knead for about 2 minutes, adding a little extra flour as needed until the dough becomes soft and only slightly sticky.
Divide the dough into four equal pieces.
Roll each piece into an 8-inch rope about 1¼ inches thick, then pinch the ends together to form bagels.
Arrange the Greek Yogurt Bagels on the prepared baking sheet.
Brush each bagel with the beaten egg.
Sprinkle generously with everything bagel seasoning.
Bake for 28–35 minutes, or until the tops are beautifully golden brown.
Allow the bagels to cool for a few minutes before serving warm.