While they are drying up a bit, prepare your deep fryer or pot with ⅓ oil or just enough that the doughnut can float comfortably. The temperature must read 365-375 degrees before you can start frying.
While the oil heats up, make the simple sugar glaze by whisking the powdered sugar, vanilla, salt, and 2 tablespoons of hot water until smooth. Add more water as needed for a honey-like consistency.
Now that the oil is 365 degrees: very carefully, lift the dough balls from the baking sheet into the hot oil. If the dough is difficult to handle, then cut the parchment paper around the balls and throw together in the pot. The parchment paper will unstick and float up.
Fry for a minute on each side, or until golden. Chopsticks are the easiest tool to flip the doughnuts over. Keep adjusting the heat to maintain temperature. Well-risen doughnuts will have a pale band around the middle. This is called the fry line.
Shake off the excess oil and roll immediately in the glaze and then the graham cracker crumbs. Transfer the crumb coated doughnuts to a wire rack and let the doughnuts cool for 5 minutes.
Add strawberry jam to a large piping bag with a metal tip and a pea-sized opening (about ½ an inch) Make a small hole in the side of the doughnuts with a chopstick and give it a slight wiggle to make room for the jam.
Press the metal tip into the opening and pipe about 2 tbsp -until the filling is just about to come out.
Serve asap, doughnuts are best the day of!