1 .Preheat the oven to 350°F. Lightly grease (or line with parchment paper) a baking sheet.
In a medium-sized bowl, beat together the butter, sugar, salt, cream of tartar and baking powder until well-blended.
Beat in the lime juice and the egg. Blend in the flour thoroughly. Dough will be very crumbly as you begin mixing- keep mixing until it is completely combined and smooth.
Roll the dough into 1" balls.
Bake the cookies for 15 to 18 minutes, until the cookies are browned on the bottom.
Cool cookies for 5 minutes and transfer to wire cooling rack. Place the wire rack over a baking sheet for easier clean up.
For the glaze: Whisk together lime zest, lime juice, and powdered sugar.
When the cookies are cool enough to handle and not fall apart, dip the tops of the cookies in the glaze and return to the cooling rack.
Roll the glazed cookies in the powdered sugar. Repeat if desired.