Preheat your oven to 375°F (190°C) and line a baking sheet with parchment paper.
In a large mixing bowl, combine the flour, baking powder, baking soda, and salt. Mix well.
In another bowl, whisk together the cottage cheese, egg, honey, and olive oil until smooth.
Pour the wet ingredients into the dry ingredients and stir until a dough forms. If using, fold in the shredded cheddar cheese.
Turn the dough out onto a lightly floured surface and knead gently for about 1 minute until smooth.
Divide the dough into 6 equal portions. Roll each portion into a ball and then poke a hole in the center to form a bagel shape.
Place the bagels on the prepared baking sheet. If desired, sprinkle sesame seeds or everything bagel seasoning on top.
Bake in the preheated oven for 20-25 minutes, or until golden brown.
Allow the bagels to cool slightly on a wire rack before serving.