Line a fine-mesh strainer with several layers of cheesecloth and set it over a bowl. Spoon the 15 ounces whole milk ricotta into the cheesecloth-lined strainer. Let drain for at least 20 minutes, then gather the cheesecloth and gently squeeze to remove any remaining liquid. Transfer the strained ricotta to a mixing bowl.
Add the 1 cup mascarpone cheese, 1 ½ cup powdered sugar, 1/2 teaspoon vanilla extract, and 1 teaspoon orange zest to the bowl with the strained ricotta.
Beat the mixture until just combined and smooth. (Use an electric mixer with a paddle attachment on low–medium speed, a hand mixer, or a whisk — stop as soon as the mixture is homogenous to avoid overmixing.)
Stir in the 1/2 cup mini chocolate chips and the 1/4 cup chopped pistachios, if using, until evenly distributed.
Transfer the dip to a serving bowl and sprinkle a few extra mini chocolate chips and chopped pistachios on top, if desired.
Cover and chill in the refrigerator until ready to serve.
Serve with cannoli shells, waffle cones, graham crackers, or your preferred dippers.