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Place the first 7 ingredients into a food processor (all of the dry ingredients plus the lime zest). Pulse until evenly combined.
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Add the cold butter and pulse until the mixture resembles coarse cornmeal.
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In a small bowl, whisk together the egg, sweetened condensed milk and vanilla bean paste. With the food processor running, pour the wet mixture into the food processor and let run until the dough starts to come together.
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Dump the dough onto a clean work surface and gently knead until it comes together in a smooth ball.
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Divide the dough in 2 equal pieces and then roll each piece into a 2-inch diameter log. Roll each log tightly in plastic wrap and place in the fridge to chill for a minimum of 20 minutes and up to overnight.
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When you are ready to bake, preheat the oven to 325 F and line a baking sheet with a silicone mat or parchment paper. Place the 1/2 cup confectioners' sugar into a shallow bowl.
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You may find it easier to work with 1/2 a log at a time, in which case slice a log in half and place the remaining half back into the fridge.
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Roll the log in the sanding (or sparkling) sugar, coating the outside thoroughly so that each cookie's edge is coated in sugar.
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Slice off 1/4-inch rounds of dough, lightly dip one side in the confectioners' sugar, and then place them confectioners' sugar side up on the prepared baking sheet, 2 inches apart.
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Dip your cookie stamp into the confectioners' sugar and then press each cookie down to engrave it and flatten it just a bit. Dip your stamp into the confectioners' sugar after each cookie, to help prevent sticking.
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Bake for 10-12 minutes, or until barely golden at the edges.
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Let the cookies cool completely; if desired, sift a little confectioners' sugar over the cookies before serving, as that will highlight the design of the stamp.