If using Homemade Cannoli Shells, prepare dough. If necessary, place ricotta cheese in a sieve or colander lined with two layers of 100-percent-cotton cheesecloth set over a bowl; strain for at least 1 hour. Discard liquid.

In a medium bowl, stir together ricotta cheese, the 3/4 cup powdered sugar, vanilla and rum, if you like, until almost smooth. Stir in 1/2 cup chocolate pieces. Cover and chill filling for at least 2 hours.

On a lightly floured surface, roll each dough portion to slightly less than 1/8-inch thickness. Using a knife and paper pattern, cut dough into twelve ovals 6 inches long and 4 inches wide. (Do not reroll trimmings.) Beginning with long side, roll dough oval loosely/lightly around one end of greased metal cannoli cylinders. Moisten overlapping dough with egg white; press gently to seal.

In a 3-quart saucepan or deep-fat fryer, heat 3 inches vegetable oil to 375°. Fry cannoli shells, a few at a time, for 1 to 2 minutes or until golden brown. Using tongs, carefully and gently lift shells from hot oil; drain any hot oil that is in metal cannoli cylinders back into pan. Drain on paper towels. Cool. When cannoli shells are cool enough to handle, remove from metal cylinders. Cool tubes before reusing. (You will need 3 or 4 cannoli cylinders.) Cool the shells completely before filling.

Just before serving, spoon filling into a decorating bag fitted with a 1/2-inch round tip (or spoon filling into a resealable plastic bag; seal bag. Snip off a small corner of the bag). Pipe filling into Homemade Cannoli Shells or the purchased shells. Arrange on a serving platter. Sprinkle additional powdered sugar over the filled shells. Sprinkle additional mini pieces over filling on ends. Serve immediately.