For filling, in a medium bowl, stir together ricotta cheese, powdered sugar, and vanilla until almost smooth. Stir in 1 ounce bittersweet chocolate. Cover and chill up to 6 hours.
Meanwhile, in a small saucepan, heat and stir 4 ounces bittersweet chocolate and the shortening over low heat until melted. Remove from heat. Transfer to a small bowl. Dip both ends of the cannoli shells in chocolate, letting excess drip off. Sprinkle chocolate ends with pistachio nuts. Place on a wire rack placed over waxed paper to dry (about 45 minutes).
When chocolate is dry, in a medium bowl, beat whipping cream at medium speed of an electric mixer or with a wire whisk until stiff peaks form. Fold into the ricotta mixture. Spoon filling into a decorating bag fitted with a large round or open star tip (or spoon into a resealable plastic bag; seal bag. Snip off a small corner of the bag). Pipe filling into shells. Cover and chill up to 2 hours. Makes 12 servings.
For chocolate cannoli:
Prepare Cannoli as directed, except stir 1/4 cup unsweetened cocoa powder in with the ricotta cheese.