In a 6 qt pot, heat the oil to 350°F-375°F. Insert a deep-fry thermometer to ensure you maintain an accurate temperature.
If you notice that the discs of dough has shrunk during handling, re-roll a bit more to stretch it out. Wrap the circle of dough around the cannoli tube, and brush a small amount of the reserved, whisked egg white onto the edge of the dough.
Wrap the dough around the tube overlapping and pressing firmly onto the dough that's been brushed with the egg white. Be sure to press firmly, or the shell will open once during frying.
Fry the shells in batches of four for 4-5 minutes, or until they float up to the surface of the oil and are a dark golden brown.
Use tongs to remove the shells from the oil, and transfer them to a cooling rack placed over a cookie sheet to allow them to drain of excess oil.
Once cooled enough to handle, carefully push the tubes from the center of the shells. You can continue re-rolling the dough and frying until all your dough has been used up.
Once all of your shells have been fried and completely cooled, you can fill them, or store them in an air-tight container for up to 2 days.