Place ricotta cheese into the center of a large piece of cheesecloth and squeeze out any excess liquid. You want the ricotta cheese as dry as possible. Place into the bottom of a high powered blender.
Add in powdered sugar, lemon zest, vanilla, and heavy cream and blend, stopping to stir frequently, until completely smooth OR until the desired consistency is reached.
Spoon filling into a disposable piping bag, cut the corner off and fill each cannoli.
Sprinkle mini chocolate chips onto filling at each end of cannoli and then sprinkle with powdered sugar.
Store refrigerated in an airtight container for up to two days.
Please please please keep in mind that not draining or getting rid of that extra liquid in the cheese will not give you the results you're looking for. I didn't drain my first few versions of my cannoli filling and after 20-30 seconds in the blender, it was pretty thick and decent, but blending it beyond 60 seconds turned it into liquid. Just FYI :)
I piped the filling with a disposable pastry bag because they're easier/sturdier to use than a regular Ziploc bag, though those will work in a pinch too.