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

In a large bowl, using a stand mixer or hand mixer, cream together the softened butter and granulated sugar on medium speed until light and fluffy, about 2-3 minutes. Scrape down the sides of the bowl as needed.

Beat in the large egg and vanilla extract until well combined. The mixture might look a little curdled, but don't worry, it'll come together.

In a separate medium bowl, whisk together the all-purpose flour, unsweetened cocoa powder, baking soda, and salt. Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined and a soft dough forms. Be careful not to overmix.

On a lightly floured surface or between two sheets of parchment paper, roll out the dough to about 1/4-inch thickness. Use a 2-inch square or round cookie cutter to cut out shapes. Carefully transfer the cut cookies to the prepared baking sheets, leaving about 1 inch between them. Bake for 6-8 minutes, or until the edges are set and the centers are still slightly soft. Let cool on the baking sheets for 5 minutes before transferring to a wire rack to cool completely.

Once the cookies are completely cool, place a scoop (about 1/4 cup) of slightly softened vanilla ice cream onto the flat side of one cookie. Gently top with another cookie, pressing down slightly to spread the ice cream evenly. Use an offset spatula or knife to smooth the edges if desired.

Place the assembled ice cream sandwiches on a baking sheet lined with parchment paper and freeze for at least 2 hours, or until firm. Once firm, you can wrap individual sandwiches in plastic wrap or foil and store them in an airtight container in the freezer for up to 2 weeks.