First, blend together all of the remaining ingredients - starting with blending the butter and brown sugar, then slowly adding the flour, then the vanilla and chocolate chips. Set aside.
Next, whip up your whipping (heavy) cream with a mixer for at least 4 minutes, until soft peaks form.
The cream will go through several stages, from bubbly, to slightly thickened, to rippling, and finally puffy and airy.
Gently stir in the sweetened condensed milk, along with the vanilla extract. You don't want to deflate the cream, so avoid overmixing.
Crumble in pieces of the no-bake cookie dough into the ice cream, folding the mixture over carefully. Reserve about 1/3 to 1/2 cup of the dough to sprinkle over top of the ice cream.
Pour the ice cream mixture into a clean loaf pan or casserole dish lined with parchment paper. Smooth it out into an even layer with the back of a spoon or an offset spatula.
Cover with tinfoil or plastic wrap and freeze for 4 hours or overnight.