For the sauce: In a small saucepot set over medium heat, add the sugar, corn syrup and 1/4 cup water, and cook until the sugar starts to bubble and turn brown, 10 to 12 minutes. Remove the saucepot from the heat. Add the heavy cream slowly and carefully to the caramel mixture (it will bubble up). When the bubbling slows, stir with a wooden spoon and add the sea salt.
For the doughnuts: Combine the cottage cheese, flour, baking powder, granulated sugar, salt, eggs and orange zest, and set aside.
Heat the oil in a large saucepot set over medium-high heat until a deep-frying thermometer inserted in the oil reaches 350 degrees F.
Scoop the dough using two spoons to make a round ball, 6 to 8 in total. Carefully drop the doughnut holes in the oil and fry until golden brown and floating, turning occasionally to ensure all sides cook evenly, 4 minutes.
Remove the doughnuts from the oil with a slotted spoon and place on a paper-towel-lined-plate to absorb any excess oil.
Spread some warm caramel sauce on each serving plate. Pace the doughnuts over the sauce and sprinkle with confectioners' sugar to serve.
Drop the doughnut holes directly above the oil instead of dropping from a distance to avoid splashing the hot oil.