The combination of fresh blueberry ice cream with sweet and tart lemon cookies tastes like a beautiful summer day with every bite. Not only does this sandwich taste wonderful, but it also looks just as great. The ice cream is a brilliant violet color and you can actually see flecks of yellow lemon zest in the cookies. Make these for your next summer cookout — they’re sure to be a hit.
To make a blueberry purée, place the blueberries, lemon juice, and ¾ cup sugar in a large saucepan set over medium-high heat. Bring the mixture to a boil, then reduce heat to a simmer and cook, stirring often, until the sugar is dissolved and the berries are soft, about 7 minutes. Let cool slightly, then carefully purée the mixture in a blender or food processor until smooth, about 30 seconds to 2 minutes. Strain the mixture through a fine strainer to remove seeds and skins. Blueberry purée can be stored in an airtight container in the refrigerator for up to 3 days. If using right away, set aside.
Prepare an ice bath by filling a large bowl with ice cubes and 1 to 2 cups of water. Place a medium bowl fitted with a fine strainer inside the ice bath.
In a clean medium saucepan, combine the blueberry purée, milk, cream, salt, and vanilla. Set over medium heat, stirring occasionally, until the mixture is warm and begins to steam, about 5 minutes.
In a medium bowl, whisk together the egg yolks and the remaining ¼ cup sugar. Carefully whisk 1/2 of the warm milk mixture into the egg yolks, 1 ladleful at a time, until the egg mixture is warmed. Whisk the egg-milk mixture back into the saucepan. Cook the mixture over medium heat, stirring constantly, until the mixture is thick enough to coat the back of the spoon and registers around 175 degrees on an instant-read thermometer, about 5 to 7 minutes. Be careful not to boil the mixture.
Immediately strain the mixture through the fine strainer into the prepared ice bath. Cool the custard in the ice bath, stirring often. Press plastic wrap against the surface of the custard and refrigerate until chilled, about 4 hours or up to 1 day.
Pour the custard into an ice cream maker. Freeze according to the manufacturer’s directions. During the last minute of freezing, add the vodka. Transfer to an airtight container, press plastic wrap against the ice cream, and freeze until it is firm, at least 2 hours.
Preheat the oven to 350 degrees. Line large baking sheets with parchment paper or silicone baking mats.
In a medium bowl, whisk together the flour, salt, and baking soda.
In a large bowl, beat the butter and sugar on medium-high speed until well combined and smooth, about 1 to 2 minutes. Add the lemon zest and lemon juice, beating until combined. Add the egg and vanilla and beat until combined. On low speed, gradually add the flour mixture and beat until combined.
Scoop the dough into 2 tablespoon-sized balls and place on prepared baking sheets.
Bake for about 10 minutes, or until the cookies are set and begin to brown at the edges. Let the cookies cool completely. Freeze the cookies until frozen, at least 1 hour. Cookies can be stored in airtight containers in the freezer for up to 1 month.
To assemble, top 1 cookie with a scoop of ice cream. Place another cookie on top of the ice cream and gently press down to form a sandwich. Repeat for remaining cookies. Freeze for at least 1 hour before serving.