Preheat oven to 350°.
While the oven is preheating make the cookie dough. Cream together the butter and sugar until light and fluffy.
Scrape the sides, add in the eggs and vanilla. Beat until mixed.
Scrape the sides and add in the flour, baking powder and cornstarch. Mix until thoroughly combined.
Use a scoop to create equal sized cookies. Double scoop the cookie dough to make large bakery style cookies (more details given above).
Flatten the cookie dough by gently pressing the bottom of a drinking glass down on the center of the cookie dough. I like to dip the glass into sugar first, but this isn't required.
Repeat with remaining dough. The cookies will spread slightly so make sure to leave room. I tend to only put 6 cookies per pan.
Bake at 350° for 9-11 minutes or until the centers of the cookies have puffed up and are no longer glossy.
To make the frosting, cream the butter until smooth. Slowly add in the powdered sugar, milk and lemonade mix. Mix until smooth and creamy. Adjust the lemonade mix amount to your liking. I tend to put all of the 2 tbsp in because I like it extra tangy.
Scoop a generous amount onto each cooled cookie. One at a time, spoon approx 1/2 tsp of raspberry syrup or jam onto the frosting and use the back of a spoon to spread the frosting around the cookie while swirling in the raspberry syrup or jam.
Refrigerate until ready to serve. Will stay fresh for 2-3 days.