Place the vegetable oil in a large, heavy pot and heat over medium-high heat until 350°F. Meanwhile, place the egg white in a small bowl and lightly beat with a fork. Line a baking sheet with paper towels and fit a cooling rack over it.
Vegetable oil, 1 large egg white
Divide the dough into 2 pieces. Roll and cut 1 piece at a time, keeping the remaining dough covered so that it doesn't dry out. Dust a work surface with flour, then use a rolling pin to roll the dough out until ⅛-inch thick. (Alternatively, you can use a pasta roller to roll the dough into a thin, even sheet, working from 1 to 5 on the machine’s dial.)
Use a 4 to 5-inch round cookie cutter to cut rounds from the sheet of dough.
Use a fork to “dock” and poke holes in each round on both sides (this prevents large bubbles that will slip the dough off the cannoli molds).
Wrap one round of dough loosely around a cannoli mold. Brush one end of the dough with egg white, pull the other end around the mold until it overlaps slightly, and press down to seal. Repeat rolling, cutting, and wrapping the remaining dough, gathering the scraps of dough and re-rolling as needed, until you have 16 shells.
Fry in batches of 4-5, adjusting the heat as needed to maintain an oil temperature of about 350°F. Using tongs, carefully lower the cannoli shells on their molds into the oil. Fry, turning as needed, until evenly golden brown, 2-3 minutes.
Remove the fried shells to the cooling rack. Cool the shells completely before filling. When the shells are cool enough to handle (about 10 minutes), remove the molds: Gently squeeze a mold together to release the shell, then slip the shell off. Cooled shells can be stored in an airtight container at room temperature for a few weeks.
Fill the cannoli shells just before serving. When ready to fill and serve the cannolis, transfer the filling into a pastry bag or Ziplcok bag and cut a ½-inch diameter piece off the end/corner. Insert the tip into one end of a shell and pipe the filling in, filling it halfway, then pipe the rest in from the other end. Dip the ends with the filling into more mini chocolate chips, if desired, and dust the filled cannolis with powdered sugar before serving.
Chopped pistachios