Preheat oven to 375°F and line a large baking sheet with parchment paper. In a large bowl, whisk together the flour, baking powder, and salt.
Add Greek yogurt and mix with a spatula until combined, then knead with your hands until a dough forms. Knead about 20 times. The dough should be soft but not sticky. Cover with a towel and let rest for 10 minutes.
Lightly flour your work surface, then place the dough on it. Roll it into a log and cut into four equal pieces. Roll each piece into a rope and connect the ends to form a bagel shape. Pinch the ends together to seal.
Place the shaped bagels on the prepared baking sheet. In a small bowl, whisk the egg and brush it over each bagel. Sprinkle with everything bagel seasoning, sesame seeds, poppy seeds, or onion flakes, if desired.
Bake for 25 minutes, or until the bagels are golden brown and puffed. Remove from the oven and let rest for 15 minutes before slicing.