In a large mixing bowl, cream butter and sugars on medium speed.
Add dry pudding and mix well. Add eggs and vanilla and beat until combined. Mix in flour and baking soda. Dough will be thick.
Using cookie scoop place cookies on prepared cookie sheet. Using bottom of a flat glass, lightly press cookie until flat.
Bake cookies for approximately 10 minutes. Remove from oven. Cool for 5 minutes on cookie sheet then remove to cooling rack.
While cookies are cooling, prepare powdered sugar glaze by whisking powdered sugar, milk and vanilla extract until smooth. Using a spoon or piping bag drizzle glaze over cookies.