Melt butter and cream with brown sugar and sugar in a large bowl.

Add egg, egg yolk, and vanilla extract. Beat well until combined.

Add flour, baking powder, and salt. Beat until just combined.

Stir in chocolate chips.

Refrigerate 1 cup of cookie dough for ice cream.

Whip whipping cream until light and fluffy. Set aside.

In a separate bowl, beat eggs and egg yolks.

Add sugar, flour, baking powder, salt, and vanilla extract. Beat until combined.

Fold whipped cream into the egg mixture until fully incorporated and smooth.

Pour mixture into a 12-cup container or divide among smaller containers.

Freeze for 2-3 hours until thickened.

Pinch off marble-sized chunks of refrigerated cookie dough.

Fold cookie dough chunks into thickened ice cream mixture with a spatula.

Continue folding until the ice cream has a uniform cookie dough color.

Return ice cream to the freezer and freeze overnight or until firm.