Preheat oven to 375 degrees Fahrenheit and line a baking sheet with parchment paper.
In a large mixing bowl, combine self-rising flour and Greek yogurt until a thick dough forms.
Transfer dough to a floured surface and knead by hand for 2 to 3 minutes until the texture is smooth and no longer sticky.
Divide the dough into 4 equal sized balls.
Roll each ball into a rope approximately 6 inches long and join the ends to create a ring shape.
Place rings on the baking sheet and brush the surface of each with the beaten egg wash.
Top each bagel with everything bagel seasoning.
Bake for 22 to 25 minutes or until the exterior is golden brown.
Allow bagels to cool on a wire rack for 10 minutes before slicing.