Apricot Sherbet

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