Cream together the butter and sugars until light and fluffy.
Add in the vanilla. Stir until combined.
Add in the flour and chocolate chips. Stir until combined.
Scoop rounded teaspoons onto a baking sheet, leaving enough room between them so that they aren't touching.
Freeze the cookie dough in the freezer until firm, about 3 hours.
For the Ice Cream
Combine sugar, vanilla, cream and half and half, mixing until sugar is mostly dissolved.
Use in ice cream maker according to manufacture's instructions.
When ice cream is finished in the ice cream maker, add in the frozen cookie dough and let mix in the ice cream maker for about 1-2 minutes longer.
The ice cream will be soft when it is finished in the ice cream maker. For more firm ice cream, place in the freezer for 3-4 hours.
Milk can be substituted in place of the half and half but the ice cream will not stiffen as much in the ice cream maker and it will be slightly icier. The heavy cream should not be substituted.To remove the caviar from a vanilla bean, gently slice through the top skin lengthwise, lay your knife crossways along the bean so the skin is flattened, and gently scrape down the length of the bean, removing the caviar as you go.