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1
In the bowl of a stand mixture using the paddle attachment, or in a large bowl using a hand mixer, beat the butter, one-half cup plus 1 tablespoon sugar, eggs and vanilla at medium speed until well incorporated, about 2 minutes (it will not be fluffy).
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2
Meanwhile, grind the coconut in a food processor until finely chopped, about 10 seconds (you should have a scant 1 2/3 cups).
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3
In a medium bowl sift together the flour, salt and baking soda.
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4
Mix the combined dry ingredients, one-half at a time, into the butter mixture until thoroughly combined, scraping down the sides of the bowl as needed.
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5
Add the coconut, mixing well.
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6
Divide the dough in half, wrap each half in plastic wrap, and flatten into a disc (the dough will be very sticky).
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7
Chill for 2 hours or longer to firm the dough.
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8
Heat the oven to 375 degrees.
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9
Place the remaining two-thirds cup of sugar in a small bowl.
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10
Using one round of dough at a time (keep the rest chilled), shape the dough into 1-inch balls and roll in the sugar.
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11
Place the dough 2 inches apart on a lightly buttered baking sheet.
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12
Lightly grease the bottom of a pint glass, or similar glass, with a little butter, then dip the glass into the sugar to coat.
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13
Press the cookie with the bottom of the glass until it is about one-eighth inch thick and 2 1/2 inches wide.
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14
Repeat with all the balls, and make sure the glass is well-sugared each time before pressing, as the dough will be sticky.
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15
Repeat with the second half of the refrigerated dough, forming and pressing the balls.
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16
Bake the cookies, one pan at a time and in the center of the oven, until they are lightly golden on the edges but still white in the middle, about 10 minutes.
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17
Rotate the pan halfway through for even baking.
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18
Remove the cookies immediately to a wire rack to prevent them from sticking to the baking sheet.
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19
Cool completely.
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20
To assemble, spread one-third cup ice cream (slightly softened) over the bottom of one cookie, and carefully top with another cookie.
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21
Press firmly but gently to avoid breaking the cookies.
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22
Run a knife or offset spatula around the edges to clean up any ice cream hanging over the edge.
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23
Freeze for at least 1 hour to firm the ice cream.
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24
Repeat with all the cookies.
