In a mixing bowl, cream together butter, granulated sugar, and brown sugar until light and fluffy. Add egg and vanilla extract, mixing well. Gradually incorporate flour, baking soda, and salt until smooth.

Preheat oven to 350°F (175°C). Line a baking sheet with parchment paper. Drop spoonfuls of cookie dough onto sheet, spacing them 2 inches apart. Bake for 10-12 minutes until edges are golden.

Allow cookies to cool on the baking sheet for 5 minutes before transferring to a wire rack for 15-20 minutes.

Spread a layer of Nutella on the bottom side of a cooled cookie. Add strawberry slices and softened ice cream, then top with another cookie.

Freeze the assembled sandwiches for at least 30-60 minutes to firm up the ice cream.

Serve the sandwiches straight from the freezer or store in an airtight container for up to one week.