Using paddle attachment of your stand mixer (or using your hand mixer) beat together room temperature butter until smooth and creamy.
Add in the powdered sugar, flour, cornstarch and vanilla and mix until combined.
The dough should come together on it's own, if not just use your hands to bring it together.Now, take a baking sheet lined with parchment paper.
Transfer the dough into a piping bag lined with a closed star tip/nozzle and pipe the cookie dough into these rosette shapes (starting from the center and making one full round around it).The dough might feel stiff to pipe at first but keep pressing and pipe and eventually with the warmth of your hands, it will loosen up and you will be able to pipe easily.Once the cookies are piped, transfer the baking sheet into the refrigerator for 2-4 hours. This will help in preventing the cookies from spreading in the oven.
Pre-heat oven to 350 F degrees. Take the baking sheet out of the refrigerator and bake at 350 F degrees for 18 to 20 minutes until the bottom of the cookies start turning light brown in color. I baked mine for 20 minutes.Transfer onto a wire rack to cool completely. Enjoy these eggless Danish Butter Cookies with coffee.
Chill the cookies for a minimum of 2 hours to prevent spreading. You can even chill overnight.