Drain whole milk ricotta cheese in a cheesecloth-lined sieve over a bowl in the refrigerator for at least 4 hours to remove excess whey.
Whisk all-purpose flour, granulated sugar, ground cinnamon, and salt together in a bowl. Cut in cold unsalted butter until crumbly, then pour in sweet Marsala wine and white vinegar, kneading for 5 minutes until a smooth, firm dough forms.
Wrap the dough tightly in plastic wrap and let it rest at room temperature for 45 minutes. Divide the rested dough into two pieces and roll out on a lightly floured surface until paper-thin, about 1/16-inch thick.
Cut out 4-inch circles with a round cutter, wrap each circle snugly around an aluminum cannoli form, and seal the overlapping edges with a small dab of water, pressing firmly to secure.
Heat vegetable oil in a deep pot to 360°F (180°C). Fry the wrapped shells 2 at a time for 2 to 3 minutes until golden and bubbly, then drain on paper towels and slide the metal tubes out while warm.
Beat the drained ricotta, powdered sugar, ground cinnamon, and vanilla extract with a hand mixer on low speed until smooth and creamy, then fold in mini chocolate chips.
Transfer the ricotta filling to a piping bag fitted with a large round tip and pipe into both ends of each cooled cannoli shell just before serving.
Dip the exposed filling ends into chopped pistachios and dust the filled shells with powdered sugar.
