For the sauce: In a small saucepot set over medium heat, add the sugar, corn syrup, 1/4 cup water and 1/8 teaspoon sea salt 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 1/4 teaspoon sea salt. Let cool enough to taste, taste and add more salt if necessary.
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 one tester ball, then carefully drop it in the oil and fry until golden brown, about 2 minutes. Cool slightly and taste, then add more granulated sugar and orange zest to the dough if desired. One at a time, scoop the remaining dough into balls (6 to 8 total) and carefully drop into the oil. Fry, turning occasionally to ensure all sides cook evenly, until golden brown and floating, about 4 minutes.
Remove the doughnut holes from the oil with a slotted spoon and place on a paper-towel-lined-plate to absorb any excess oil.
Transfer the doughnut holes to a platter and dust them with confectioners' sugar. Serve with the caramel sauce on the side.
Drop the doughnut holes directly above the oil instead of dropping from a distance to avoid splashing the hot oil.