To Make the Ice Cream

Heat the cream, milk, ½ cup of the sugar, and the peanuts in a heavy saucepan over medium heat, stirring occasionally, until almost simmering, about 5 minutes. Turn off the heat, cover, and let the peanuts steep in the liquid for 10 minutes. Whisk together the egg yolks, the remaining ¼ cup sugar, and the salt in a bowl. Slowly pour the cream into the egg mixture, whisking as you pour.

Return the mixture to the saucepan. Cook over medium-low heat, stirring constantly with a heat-resistant plastic or wooden spatula, until the custard reaches 175°F and lightly coats the spatula.

Strain the custard into a clean bowl, discarding the peanuts. Cool over an ice bath until room temperature. Whisk in the peanut butter. Refrigerate for 4 hours or up to overnight. Churn in an ice cream machine according to the manufacturer’s instructions. Freeze until scoopable, about 4 hours, depending on your freezer.

To Make the Cookies

Preheat the oven to 350°F. Line 3 baking sheets with parchment paper.

In a large bowl, beat together the butter and the granulated and brown sugars until smooth and creamy. Stir in the vanilla extract and the egg. Sift together the flour, baking soda, and baking powder. Add the salt. Stir the dry ingredients into the butter mixture. Stir in the coconut, peanuts, oats, and chocolate chips.

Using about 1½ tablespoonfuls for each cookie, place mounds of the cookie dough 3 inches apart on the prepared pans. Bake until golden brown, about 12 minutes. Let the cookies cool to room temperature before removing them from the pans with a spatula.

In Advance

The cookie dough can be made up to 3 days in advance. The ice cream sandwiches can be made 2 days in advance. Store in an airtight container.