Preheat the oven to 350°F (175°C). Line two baking sheets with parchment paper.

In a large bowl, beat the butter with both sugars on medium speed until the mixture is pale and fluffy, about 3 to 5 minutes. Add the egg, vanilla, and salt, then mix until evenly combined.

Whisk the flour, cocoa powder, and baking soda together in a separate bowl until uniform.

With the mixer set low, gradually add the dry mixture to the wet ingredients, scraping the bowl as needed. Stir only until everything is incorporated—the dough will be very thick.

Drop rounded tablespoonfuls of dough (or use a medium scoop) onto the prepared sheets, spacing them apart. Bake 9 to 12 minutes until the cookies have puffed slightly and the tops look dry.

Let the cookies cool on the baking sheets for 5 minutes, then transfer them to a wire rack to cool completely.

Line a baking sheet or pan with parchment paper or foil. Using about 3 tablespoons per scoop, portion the ice cream into 10 balls; if you baked more than 20 cookies, make extra scoops to match.

Cover the scoops with another sheet of parchment and press each mound down so it spreads to the size of the cookies. If the ice cream softens, place the pan in the freezer for 5 to 10 minutes to firm up.

Place a flattened ice cream disk between two cooled cookies to form sandwiches. Serve right away, or individually wrap each sandwich in plastic, foil, or parchment and freeze for up to 3 months.