Preheat the oven to 350°F. Line two baking sheets with parchment paper.
In a medium bowl, whisk together the flour, baking soda, and salt. Set aside.
In a large bowl, using an electric mixer, beat the softened butter, brown sugar, and granulated sugar until creamy. Add the vanilla extract and egg, mixing until well combined.
Gradually add the flour mixture to the wet ingredients, mixing until just combined. Fold in the sprinkles.
Drop rounded tablespoons of dough onto the prepared baking sheets, spacing them about 2 inches apart. Bake for 10-12 minutes, or until the edges are lightly golden. Remove from the oven and let cool on the baking sheets for 5 minutes before transferring to wire racks to cool completely.
Once the cookies are cool, take one cookie and place a scoop of vanilla ice cream on the flat side. Add a few slices of strawberries and blueberries on top of the ice cream, then top with another cookie, flat side down. Gently press together to form a sandwich. Repeat with the remaining cookies and ice cream.
For best results, freeze the assembled ice cream sandwiches for at least 1 hour before serving to allow them to set.