Temper dough: Remove dough from fridge. Let sit at room temperature for 1 hour. This is crucial for easy rolling and maximum bubbling during frying.
Heat oil: Pour oil into heavy-bottomed pot to depth of 3 inches. Heat to 350 to 360°F. Use a thermometer and maintain this temperature throughout frying.
Prepare egg wash: Beat reserved egg white with 1 tablespoon water. Set aside with pastry brush.
Divide and roll dough: Lightly flour work surface. Divide dough into 3 to 4 portions. Keep unused portions covered with plastic wrap. Take one portion and roll with rolling pin or pasta machine. For pasta machine: flatten dough by hand into rough rectangle. Run through widest setting, then progressively thinner settings until setting 7 or 8. Dough should be 1/16 inch thick, almost see-through. For rolling pin: roll until 1/16 inch thick, rotating frequently and using minimal flour.
Cut circles: Using a 4-inch round cutter (or 3 to 5 inches for different sizes), cut out circles. You should get 5 to 6 circles per portion. Gather scraps, press together gently, let rest 10 minutes, re-roll once.
Rest circles: Let cut circles sit on counter for 5 to 10 minutes before wrapping. Work in batches of 6 to 8 circles at a time. Keep unused circles covered with plastic wrap to prevent drying.
Wrap cannoli tubes: Take one circle and place cannoli tube across the center. Wrap dough around tube, overlapping edges by ½ inch. Brush egg wash generously on one overlapping edge. Press the other edge onto it firmly, pinching and pressing the seam together along entire length. Don’t wrap too tight around tube, leave slight wiggle room. Gently flare both ends outward slightly away from tube.
Fry shells: Place 2 to 3 wrapped molds in hot oil seam-side down. They may sink, this is okay. Fry 2 to 3 minutes total, turning frequently with tongs for even browning. Shells should be deep golden brown with darker blistered spots.
Drain and remove from molds: Using tongs, lift shells from oil and place on wire rack over sheet pan. Let cool 45 to 60 seconds, just until cool enough to handle. While still warm, carefully slide shells off tubes. Let shells cool completely on wire rack. Repeat wrapping and frying with remaining dough circles, letting tubes cool briefly between batches.