To Make the Sugar Cookie Dough In a large bowl, cream together the butter and the sugar until pale and fluffy, about 2 minutes. Next, add the eggs one at a time, followed by the vanilla. Mix until just combined.
In a separate bowl, stir together the flour, baking powder, and salt.
Add the dry ingredients into the creamed butter and mix until a dough is formed.
Lay some cling wrap on your counter and spoon your dough on top and form a log about 17 inches long. Roll up the log like a sausage and chill the dough for at least 1 hour or pop in the freezer and freeze for up to 8 weeks.
Preheat your oven to 350°F (180°C). Line 2 cookie sheets with parchment paper and set aside.
Slice the cookies around ¼ inch thick. Place the cookies about 2 inches apart on the prepared cookie sheet.
Bake for roughly 10-12 minutes or until slightly golden. Remove from the oven and allow to cool completely on a wire rack.
To Make the Vanilla Icing Using a whisk, combine the powdered sugar, butter, milk, and vanilla until you have a smooth thick icing.
Color the icing with a few drops of food coloring then mix until even in color.
Using a small offset spatula or the back of a small spoon frost the cookies then scatter over sprinkles. Allow setting for about 30 minutes.
Once set, cover and store the cookies in an airtight container for up to 2 days.