Preheat the oven to 400°F and line a baking sheet with parchment paper. This higher start temperature helps the bagels set and brown quickly.
Place the cottage cheese in a food processor or high-speed blender and process until completely smooth — no visible curds — about 30 to 45 seconds. Scrape down the sides once if needed.
In a medium bowl whisk together the flour, baking powder, and salt so the leavening is evenly distributed.
Add the blended cottage cheese to the dry mixture and stir briefly to combine. Add the beaten egg and fold the mixture with a spatula until it pulls together into a soft, slightly sticky dough.
Turn the dough onto a lightly floured surface and knead gently for 1 to 2 minutes until smooth. If it feels very sticky, dust with up to 1 tablespoon extra flour, but avoid overworking it.
Cover the dough and let it rest at room temperature for 10 minutes — this short rest hydrates the flour and makes shaping easier.
Divide the dough into 4 equal pieces. Roll each piece into a tight ball, then press your thumb through the center of each ball and gently stretch to form a 1 to 1 1/2 inch hole (it will shrink a bit while baking). Place the formed bagels on the prepared pan about 2 inches apart.
Brush the tops lightly with the reserved beaten egg and sprinkle generously with Everything bagel seasoning.
Bake on the middle rack for 18 to 20 minutes, rotating the pan once halfway through, until the bagels are puffed and golden-brown on top.
Remove from the oven and transfer to a wire rack. Allow the bagels to cool for at least 20 minutes before slicing — cutting too soon can make the interior seem gummy.