Preheat your oven to 350°F.
Slice the cookie dough into rounds and arrange them on a round pizza stone or round baking pan.
Using slightly damp hands, press the dough together into one large circle. If the dough is too cold, let it sit at room temperature for a few minutes first to make it easier to work with.
Press the dough into an even layer, making sure it’s not too thick since it will rise while baking.
Bake for 15–20 minutes, checking around the 15-minute mark. Baking times may vary depending on your oven and the pan you’re using. The cookie is done when the edges are lightly golden and the center is set.
Remove from the oven and allow the cookie to cool completely.
Tint one tub of vanilla buttercream with blue food coloring.
Place the blue frosting, remaining vanilla frosting, and strawberry frosting into separate zip-top bags. Push the frosting to one corner of each bag and snip off a small corner to create a piping bag.
Pipe a blue rectangle in the upper left corner of the cookie to create the “stars” section of the flag.
Pipe alternating red and white stripes across the rest of the cookie.
Decorate with festive M&M’s and sprinkles.
Slice like a pizza and serve.