How to Make It
Prepare the Florentines: Preheat oven to 300°F. Line 2 baking sheets with parchment paper. Place pistachios and ¼ cup of the sugar in the bowl of a food processor and process until finely ground.
Combine cream, butter, and remaining 1/2 cup sugar in a medium saucepan over medium-high; bring to a boil, stirring often. Remove pan from heat; stir in ground pistachio mixture, flour, and vanilla, stirring until a smooth paste forms. Working in batches, spoon tablespoonfuls of the mixture 3 inches apart onto baking sheets lined with parchment paper (you should have 6 cookies per sheet).
Bake until bubbly and browned, 18 to 20 minutes. Cool on pans 3 to 4 minutes. While still warm, remove cookies from pans with an offset spatula, and shape each cookie around the handle of wooden spoon (or a cannoli mold if you have one). If cookies get too firm before shaping, return to oven for 1 minute to soften. Let cookies cool until set, about 5 minutes. Gently slide off spoon, and transfer to a wire rack to cool completely. Let baking sheets cool then repeat with remaining dough.
Prepare the Filling: Beat cream, powdered sugar, and salt in a large bowl with an electric mixer on high speed until stiff peaks form. Stir together ricotta, lime zest, and lime juice in a large bowl. Stir one-third of whipped cream into ricotta mixture; gently fold in remaining whipped cream. Cover and chill until ready to use.
To assemble cannoli, fill cannoli shells with ricotta mixture. Dip ends of cannoli in finely chopped pistachios. Serve immediately.