Preheat oven to 350°F. Grease a 9" pie dish and set aside.
To make the crust, combine the graham cracker crumbs and brown sugar in a small bowl. Stir in the melted butter. Press the mixture into the bottom of the prepared pan. Set aside.
Using a hand mixer or a stand mixer fitted with the paddle attachment, beat the mascarpone until creamy. Add the ricotta, sugar, sweetened condensed milk, and vanilla extract and beat for another 2-3 minutes. Stir in the chocolate chips.
Pour the filling into the prepared crust. Bake for 25-30 minutes. Cool completely, then chill in the refrigerator for at least 4 hours, or overnight.
Notes
The filling may seem like it's not fully set when you pull the pie out of the oven, but that's normal. It will set up further after chilling in the refrigerator.
I didn't have to strain the ricotta cheese I used, but if yours contains a lot of moisture, you will want to strain that moisture out.