In a medium saucepan, heat sugar, corn syrup, milk and 1 cup heavy cream on medium heat, whisking occasionally until sugar and corn syrup are dissolved.
In a small bowl, whisk together cornstarch and ¼ cup heavy cream until smooth.
Add cornstarch mixture to saucepan and whisk well.
Cook over medium high heat until mixture thickens slightly, approximately 3-4 minutes. Remove from the heat.
Whisk in mascarpone cheese, ricotta, vanilla and Fiore Di Sicilia extracts into the hot mixture until smooth.
Pour mixture into a large bowl and place over an ice water bath to cool ice cream base down quickly.
Cover ice cream base and chill for several hours or overnight.
Make Chocolate Covered Sugar Cone Pieces
In a small bowl, using a spoon, mix together the chopped sugar cones and melted chocolate chips until the cones are well coated.
Place onto a wax paper lined sheet pan and separate the pieces with 2 forks.
Place the sheet pan in the refrigerator until the chocolate is hard.
Remove the sheet pan from the refrigerator and break mixture into smaller pieces with your hands or use a sharp knife on a cutting board.
Place pieces into a small bowl and place back into the refrigerator until ready to add into the processed ice cream.
Process the Ice Cream
Process ice cream base in an ice cream machine and process according to the manufacturer’s directions.
When the ice cream is processed to the point that it is thick but flows like a soft serve, add mini chocolate chips, pistachios and chocolate covered crushed sugar cones.
Process for 1-2 minutes more until all the solid additions are well incorporated.
Using a spatula, scrape ice cream into an airtight container.
Place a piece of plastic wrap on top and cover tightly.