1 cup unsalted butter, at room temperature
1 tablespoon key lime juice
1/2 teaspoon salt
1 tablespoon grated key lime zest
1/2 cup powdered sugar
1/3 cup rice flour
1-3/4 cups all-purpose flour
lime sugar for garnish (recipe below)
In a large mixing bowl beat the butter, sugar, lime juice, salt, and one half the lime zest (1-1/2 teaspoons) until light and fluffy. Stir in the rice flour, then all-purpose flour, beating only enough to incorporate. The dough will be very soft. Divide dough in thirds. Spoon each portion onto waxed paper or plastic wrap and form a log about 14 inches long and 1-1/2 inches in diameter. Fold the paper over the log, then roll with your palms until smooth. Twist ends of the paper and refrigerate or freeze until firm, 1 to 4 hours.
To make the lime sugar, place sugar and remaining zest in a blender or coffee mill and whirl until zest is very finely minced and sugar is lightly colored, about three minutes. Strain mixture through a fine sieve, discarding any bits of peel that remain. Set aside.
Preheat oven to 300 F. Slice chilled dough into rounds about 1/4 inch thick. Place 1 inch apart on ungreased baking sheets. Lightly butter the bottom of a flat-bottomed glass and dip into the lime sugar. Press lightly onto tops of cookies, dipping the glass into the sugar mixture before pressing each cookie to prevent dough from sticking. Bake 15 to 20 minutes, until light golden. Cookies will be fragile: allow to cool five minutes on baking sheets before removing with a spatula to cool completely on wire racks.