For the ice cream:
1 cup whole milk
¾ cup sugar
2 cups heavy cream
Pinch of salt
1 vanilla bean, split in half lengthwise
6 large egg yolks
¾ tsp. vanilla extract
For the cookies:
4 tbsp. unsalted butter, at room temperature
¼ cup vegetable oil
1 cup light brown sugar
2 large eggs
1 tsp. vanilla extract
½ cup unsweetened cocoa powder
2 cups all-purpose flour
1 tsp. baking powder
¼ tsp. salt
Combine the milk, sugar and 1 cup of the cream in a medium saucepan. Heat over medium-high heat, stirring occasionally, until warmed through. Scrape the seeds from the vanilla bean into the mixture and add the husk of the bean as well. Cover the saucepan, remove from the heat and set aside to steep for 30 minutes at room temperature.
Pour the remaining 1 cup of cream into a large bowl with a fine mesh sieve set over the top. In a separate medium bowl, whisk together the egg yolks. Slowly pour some of the warm milk mixture into the bowl with the egg yolks, whisking constantly to temper the eggs. Continue until you have added all of the milk mixture. Return the mixture to the saucepan.
Stir the mixture constantly over medium heat with a heatproof spatula, being sure to scrape the bottom of the pan as you stir. Continue cooking until the mixture thickens and coats the back of a spoon (about 170-175°F.) Pour the custard through the mesh sieve and stir it into the cream. Place the vanilla bean into the custard mixture, stir in the vanilla extract, and stir until cool over an ice bath. Cover and chill thoroughly in the refrigerator.
Remove the vanilla bean from the ice cream batter, stir well, and freeze in your ice cream maker according to the manufacturer’s instructions. Line a chilled 9 x 13″ pan with plastic wrap. When the ice cream has reached a soft serve consistency, spread some of the ice cream into the pan in an even layer about 1 inch thick. Freeze until firm.
In the bowl of an electric mixer, combine the butter, vegetable oil and brown sugar. Beat on medium speed until combined. Blend in the eggs one at a time, and the vanilla extract until smooth. In a separate bowl combine the cocoa powder, flour, baking powder and salt; whisk to blend. With the mixer on low speed, add the dry ingredients to the bowl with the wet ingredients and mix just until incorporated and a soft dough forms. Gather the dough into a disc, cover with plastic wrap and refrigerate until well chilled, at least 1 hour.
Preheat the oven to 350˚ F. Line a baking sheet with parchment paper or a silicone baking mat. On a lightly floured work surface, roll out the dough to about ¼-inch thick. Use a cookie cutter to cut out as many pieces as you can, transferring the cut outs to the prepared baking sheet. Gather and re-roll the dough scraps as needed. If desired, use a wooden skewer to make a dotted pattern on the cookies. Bake 8-10 minutes. Let cool on the baking sheet a few minutes before transferring to a wire rack to cool completely.
To assemble the sandwiches, use the same cookie cutter that was used for the cookies to cut out pieces of ice cream. Layer one piece of ice cream between two of the cookies and return to the freezer immediately. Wrap the sandwiches individually as desired. Keep frozen until ready to serve.