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1
Drop six 2/3-cup mounds mint chocolate chip ice cream onto waxed-paper-lined baking sheet.
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2
Using metal spatula, shape each mound into 3- to 3 1/2-inch square; freeze squares.
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3
Beat butter and sugar in large bowl until smooth.
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4
Beat in egg yolk and vanilla.
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5
Sift flour, cocoa and salt onto butter mixture.
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6
Stir until blended and soft dough forms.
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7
Gather dough into ball; flatten into rectangle.
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8
Roll out dough between 2 sheets of waxed paper to 13 x 10-inch rectangle.
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9
Place dough, still between waxed paper sheets, on baking sheet.
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10
Chill until firm, at least 1 hour and up to 1 day.
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11
Position rack in center of oven and preheat to 300F.
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12
Line large baking sheet with parchment paper.
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13
Peel top sheet of waxed paper off dough.
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14
Trim dough to 12 x 9-inch rectangle; cut dough into twelve 3-inch squares.
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15
Transfer squares to parchment-lined sheet, discarding waxed paper and spacing squares about 1 inch apart.
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16
Bake until cookies are firm to touch, about 20 minutes.
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17
Cool cookies completely on sheet.
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18
Melt white chocolate in medium metal bowl set over saucepan of barely simmering water, stirring until smooth (do not allow bottom of bowl to touch water).
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19
Remove bowl from over water.
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20
Holding corner of 1 cookie, dip cookie into melted chocolate until half covered on diagonal, tilting bowl if necessary to submerge.
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21
Shake cookie gently to allow some excess chocolate to drip back into bowl.
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22
Return dipped cookie to parchment-lined baking sheet.
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23
Repeat with remaining cookies and white chocolate.
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24
Freeze cookies until chocolate coating is firm, about 10 minutes.
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25
Arrange 6 cookies, flat side up, on work surface.
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26
Top each with frozen ice cream square, then another cookie, flat side down, pressing slightly to adhere.
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27
Cover and freeze sandwiches.
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28
(Can be made 4 days ahead.
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29
Keep frozen.)
