Preheat the oven to 350°F and line a baking sheet with parchment paper.
In a large bowl, whisk together the flour, baking powder, salt, and garlic powder.
Finely chop the chives and mince the rosemary, if you haven't already.
Add the Greek yogurt, 1 cup of the cheddar cheese (keep ¼ cup for sprinkling on top), chives, and rosemary to the bowl. Stir until a shaggy dough forms.
Transfer the dough to a lightly floured surface and add a little flour on your hands and knead gently until the dough comes together and forms a ball.
Divide the dough into 8 equal pieces.
Roll each piece into a rope about 5-6 inches long. Bring the ends together and pinch to seal, forming a bagel shape.
Place the bagels on the prepared baking sheet. Brush the tops lightly with olive oil.
Bake for 15 minutes. Remove from the oven and sprinkle the remaining cheddar cheese over the tops of the bagels.
Return to the oven and bake for an additional 5-10 minutes, or until the bagels are lightly golden and the cheese is melted.
Let cool for a few minutes before serving.