Preheat the oven to 350 degrees F.

Sift together the flour and the baking soda in a in a medium bowl and set aside. In a large mixing bowl, using a hand-held mixer, cream together the butter, brown sugar and white sugar. Beat in the instant pudding mix until incorporated.

Beat in the eggs, 1 at a time, then add the flour mixture, vanilla and the chocolate chips. Drop a spoonful of cookie mix onto greased cookie sheets. Repeat with remaining dough, leaving a little space between the cookies. Bake until the cookies are golden brown, about 10 to 12 minutes. Remove from the oven and cool on a wire rack.

When cool, put 1 scoop of vanilla ice cream on a cookie and top with another cookie to form a sandwich. Repeat with remaining cookies and ice cream. Dust with powdered sugar and serve.