Preheat the oven to 375˚F and line a rimmed baking sheet with parchment paper.
In a large bowl, combine flour and Greek yogurt. Stir with a wooden spoon until a coarse, shaggy dough forms. Scrape the dough onto a floured surface, then knead by hand for 2 to 3 minutes, or until a smooth round of dough forms. Flatten into a disc, cover with a towel and let rest for 10 minutes.
Cut into 8 equal pieces. Roll each piece of dough into a ball, then cover again and let rest for 10 minutes.
Lightly coat your hands in flour. Using your thumb, make a hole in the center of each ball of dough about 1 ½ -inch wide, pulling on the outer edge of the dough as you turn it around your thumb to form an evenly shaped bagel. Place on prepared baking sheet and repeat with remaining dough.
Lightly beat the egg with a pinch of salt. Brush the tops of the bagels with egg wash, then sprinkle with desired toppings, if using.
Bake for 25-30 minutes, or until golden brown on top.