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1
Quarter the apricots, and remove the pits.
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2
Place the apricot quarters in a food processor, and puree until smooth, about 1 minute.
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3
Transfer to a medium bowl, and add the sugar, corn syrup, and lemon juice.
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4
Whisk to combine.
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5
Cover the bowl with plastic wrap, and macerate about 1 hour in the refrigerator.
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6
Pass the apricot mixture through a fine sieve into a medium bowl; discard the solids.
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7
Whisk in the buttermilk and milk.
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8
Cover with plastic wrap, and refrigerate until chilled, about 3 hours.
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9
Freeze the mixture in an ice-cream maker according to the manufacturers instructions.
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10
Transfer to an airtight container; freeze up to 4 days.
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11
Preheat the oven to 350F.
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12
Line 2 baking sheets with parchment paper; set aside.
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13
In a food processor, pulse about 1 cup almonds with 1/2 cup sugar until the almonds are finely ground.
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14
Add the flour, and pulse until combined.
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15
Transfer to a bowl.
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16
In the bowl of an electric mixer, whisk the egg whites, salt, vanilla, and remaining 1/4 cup sugar until soft and shiny peaks form.
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17
Gently fold into the dry ingredients until just blended.
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18
Drop the batter by the tablespoon, about 1 1/2 inches apart, onto prepared baking sheets.
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19
Arrange 3 sliced almonds on top of each cookie.
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20
Bake the cookies until the edges are lightly browned, about 14 minutes.
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21
Let the cookies cool slightly on baking sheets before transferring to wire racks.
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22
Let cool completely before serving.
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23
The cookies can be stored in an airtight container at room temperature up to 1 week.
