Preheat the oven to 375°F (190°C) and line a baking sheet with parchment paper.
In a large mixing bowl, combine the self-rising flour and Greek yogurt with a spatula until a shaggy dough begins to form.
Transfer the dough to a lightly floured work surface and knead by hand for approximately 2 to 3 minutes until the dough is smooth and slightly tacky but not sticky.
Divide the dough into 4 equal-sized portions.
Roll each portion into a rope approximately 6 inches long and join the ends to form a ring, or roll into a ball and use your thumb to poke a hole through the center, stretching slightly.
Place the bagels on the prepared baking sheet and brush the top of each bagel with the beaten egg.
Sprinkle the everything bagel seasoning evenly over the tops.
Bake in the center of the oven for 20 to 22 minutes until the bagels are golden brown and firm to the touch.
Transfer to a wire rack and allow to cool for at least 5 minutes before slicing and serving.