Preheat the oven to 375 degrees Line a cookie sheet wit parchment paper or silicone baking mat. Set aside.
In a large mixing bowl, mix butter with electric mixer for 30 seconds.
Add both sugars and cream until light and fluffy, at least 3 minutes.
Add egg and vanilla and mix until smooth.
In a large mixing bowl, whisk together flour, cream of tartar and soda.
Add the dry ingredients to the wet ingredients and mix until combined. The dough will be very thick.
Scoop a heaping tablespoons of dough and roll into balls. Place the balls onto prepared cookie sheet. Dip a greased foot of a wine glass in granulated sugar and flatten the cookies.
Sprinkle the decorative sugar on top of the cookies.
Bake the cookies for 7 to 9 minutes, or until the edges just start to brown. (For us 7 minutes was the magic number).
Cool the cookies on the sheet for 2 minutes, then transfer onto a cooling rack.