Preheat oven to 350F.

In a large mixing bowl, combine the self-rising flour and Greek yogurt until it forms a ball (you may need to begin by stirring with a spoon, then switch to mixing with your hands).

Turn the dough out onto a floured surface and knead the dough for 2-3 minutes, until the dough is smooth but still tacky.

Divide the dough into 4 equal portions. Roll each portion of dough out into a 10-inch long rope. Coil the dough into a circle to form the bagel, pinching the ends of the rope together to complete the circle.

Place the bagels on a baking sheet prepared with parchment paper, a silicone baking mat, or non-stick cooking spray. Set aside.

In a small bowl, whisk together the egg and water. Brush the egg wash lightly over the top and sides of the bagels.

Sprinkle the top of the bagels with the toppings of your choice, or leave plain.

Bake the bagels at 350F for 25 minutes, or until golden brown.

Cool the bagels for 10 minutes on a wire baking rack.

Slice and serve the bagels either toasted or warmed with cream cheese, butter, or other spreads.