To prepare the cookie dough, beat together butter and sugars in a large mixing bowl with an electric mixer on medium speed until light and fluffy, 2 to 3 minutes. Beat in vanilla and milk. Add salt and flour and mix until incorporated. Stir in chocolate chips. Refrigerate until ready to cook waffles.
To make waffles, sift together four, baking powder, baking soda, and salt. In a separate bowl, lightly whisk eggs. Whisk in buttermilk, melted butter, sugar, and vanilla. Add dry ingredients and stir until just combined.
Preheat waffle maker and lightly spray with cooking spray or brush with vegetable oil. Ladle a heaping 1/2 cup of batter onto iron and quickly drop 6 to 7 marble size balls of cookie dough on top. Close lid and cook according to manufacturer's directions, until golden brown and toasted.
For the whipped cream: whisk powdered sugar, cocoa powder, and 2 tablespoons of the heavy cream in a large mixing bowl or the bowl of a stand mixer until smooth. Using the whisk attachment, gradually beat the remaining 1/2 cup heavy cream into the mixture. Continue beating until stiff peaks form. Spoon onto warm waffles and serve immediately.