Use a mixer to beat the butter and 3/4 cup of granulated sugar for 2-3 minutes until lighter in color and fluffier in texture.
Beat in the egg and vanilla for 1-2 minutes.
In a separate bowl, combine the flour, baking powder, cream of tartar, and salt. Stir into the batter until combined.
Scoop with a #40 (about 2 tablespoons) cookie dough scoop onto parchment-lined baking sheets, at least 2 inches apart.
Put 3 tablespoons of granulated sugar into a small bowl.
Moisten the flat bottom of a glass, dip it in the sugar, and use it to flatten the cookie dough balls slightly. Re-dip the glass in the sugar before flattening each ball of dough.
Bake at 350˚F for 8-10 minutes. The bottoms of the cookies should be lightly browned, but the tops should not be.