Before adding the flour, it is important to heat treat it. Add the flour into a medium-sized heat-safe bowl. Microwave the flour in two 30-second intervals, stirring after each interval. Allow the flour to cool completely before mixing it into the cookie dough ingredients.
Blend the butter and brown sugar, then slowly add the flour, the 1 teaspoon of vanilla, and the chocolate chips. Set it aside.
Whip up your heavy whipping 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 1 tablespoon 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 ⅓ to ½ 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. Sprinkle the cookie dough crumbles on top.
Cover with tin foil or plastic wrap and freeze for 4 hours or overnight.