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1
Position 1 rack in top third and 1 rack in bottom third of oven and preheat to 350F.
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2
Line 2 baking sheets with parchment paper.
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3
Mix first 5 ingredients in medium bowl.
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4
Using electric mixer, beat butter in large bowl until fluffy.
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5
Add both sugars; beat until well blended.
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6
Beat in egg and vanilla.
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7
Stir in dry ingredients.
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8
Using 2 tablespoons batter per cookie, drop 8 mounds onto each sheet, spacing mounds 3 inches apart.
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9
Flatten to 2-inch rounds.
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10
Bake cookies 10 minutes.
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11
Reverse baking sheets and bake until cookies are golden and dry to touch, about 3 minutes longer.
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12
Let cool 2 minutes.
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13
Transfer cookies to rack.
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14
Cool completely.
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15
(Can be made 1 day ahead.
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16
Store airtight.)
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17
Preheat oven to 375F.
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18
Spray large rimmed baking sheet with nonstick spray.
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19
Spread nectarines in single layer on sheet.
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20
Sprinkle with sugar; toss to coat.
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21
Bake nectarines 15 minutes.
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22
Stir well.
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23
Bake until fruit is tender and juices begin to thicken and caramelize, stirring every 5 minutes to prevent burning, about 20 minutes longer.
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24
Transfer fruit and juices to large bowl; mash coarsely; cool.
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25
Mix ice cream into fruit.
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26
Freeze until almost firm, about 45 minutes.
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27
Place 8 cookies, flat side up, on work surface.
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28
Spread 1/3 cup ice cream over each.
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29
Top each with 1 cookie, flat side down, and press gently to adhere (reserve any remaining ice cream for another use).
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30
Wrap sandwiches in foil and freeze.
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31
(Can be made 3 days ahead.
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32
Keep frozen.)
