In a large bowl combine heavy beam, half and half, condensed milk, and sugar. Mix until sugar is dissolved (2-3 minutes). Add cocoa powder and vanilla and mix another minute or two until cocoa powder is mixed in.
Freeze mixture according to ice cream machine's instructions.
While ice cream is freezing, prepare the cookie dough. Cream together butter and sugars until fluffy. Add salt, vanilla, and flour and mix until dough starts to form (it will be very crumbly). Add milk and mix (now it will look like cookie dough). Stir in chocolate chips.
Transfer ice cream to 1 or 2 shallow containers. Add a large scoop of ice cream, then a couple tablespoons of cookie dough, then more ice cream, then more cookie dough. Continue until all ice cream is in the shallow containers. Freeze 4 hours (or until ready to serve). Allow to thaw for a few minutes before serving.