Place the flour in a microwave-safe bowl and heat it for 1 minute. Let it cool.
In a separate bowl, beat the softened butter with the brown sugar and granulated sugar until the mixture is creamy and light. Add the cream or milk and vanilla extract, then beat again.
Mix in the flour and salt until just combined. Stir in the mini chocolate chips.
Roll the dough into small balls and place them on a plate or baking sheet lined with parchment paper. Freeze for 10-20 minutes.
Crust:
Crush the Oreos into fine crumbs using a food processor, blender, or by placing them in a ziploc bag and rolling over them with a rolling pin. Mix the melted butter with the crumbs using a fork until evenly moistened.
Press the mixture into the bottom and partway up the sides of a 10-inch springform pan using a glass or a flat-bottom measuring cup. Set aside.
Filling:
In a large bowl, beat the softened cream cheese, granulated sugar, and 2 tablespoons of flour with a hand mixer until smooth.
Add the eggs, sour cream, and vanilla extract. Mix on low speed for 10-15 seconds, then scrape the sides and bottom of the bowl. Mix again just until smooth, being careful not to overmix the batter.
Pour half of the filling into the prepared crust.
Add most of the frozen cookie dough balls and mini chocolate chips to the remaining cheesecake batter, reserving some for decorating. Stir to combine, then spoon this mixture over the top of the plain cheesecake filling.
Wrap the bottom of the springform pan in a plastic slow cooker liner or two layers of foil. Place the cheesecake in a larger pan and carefully pour water around the edges to create a water bath, if using.
Bake the cheesecake for 80-90 minutes with a water bath or 60-70 minutes without a water bath, until the edges are set but the center jiggles slightly.
Turn off the oven and crack the door open, propping it if needed. Let the cheesecake cool slowly for 30-60 minutes.
Remove the cheesecake from the oven and cool completely on a wire rack. Refrigerate until fully chilled before slicing.
Decorate with sweetened whipped cream, reserved cookie dough balls, and mini chocolate chips as desired.