Preheat oven to 350℉. Place the potato rounds into a bowl, cover with water, and set aside.
Place the flour, brown sugar, salt, and butter in a food processor and pulse to break up the butter. Next, add the cottage cheese and pulse to combine. It should look crumbly, but not wet.
Turn the processor on and slowly add cold water, 1 tablespoon at a time. Once a ball has started to form, you can stop. Set aside.
Heat the olive oil in a skillet over medium heat. Add the breakfast sausage and break apart into larger chunks. Cook for 2-3 minutes to brown the sausage. Remove from heat and set aside.
Transfer the dough to a floured work surface. Roll dough into a 10-12 inch circle.
Remove the potatoes from the water and pat each round dry. Place the potato slices in the center of the circle, leaving roughly a 1.5-inch border. It is okay for them to overlap.
Top the potato slices with the breakfast sausage, bell pepper, onion, and shredded cheddar cheese.
Fold the border towards the center of the galette. Then, make 4 wells in the galette to place the eggs.
Crack 1 egg in each well. Some eggs may drip down the sides, but that is ok.
Bake the breakfast galette for 15-20 minutes or until desired egg doneness. The bottom of the crust should be golden brown, and the egg whites should be fully cooked.
Remove from the oven and allow to sit for 5 minutes before serving