Preheat the oven to 350° F. Spray an 11x17 inch jelly roll pan with nonstick cooking spray and line with parchment paper.
Add egg whites and cream of tartar to a large mixing bowl and beat with an electric mixer until fluffy, about 2 minutes. Add sugar and beat until glossy and stiff peaks form, about 1 minute. Set aside.
In a separate bowl, mix egg yolks, flour, baking powder, milk, and vanilla extract until smooth. Gently fold into the egg white mixture using a rubber spatula.
Scoop two 1/4 cup portions of batter into separate bowls. Add red dye to one and blue to the other and stir to combine.
Spread the remaining undyed batter into the prepared pan. Dollop the colored batters randomly over the top and swirl with a skewer. Tap the pan on the counter to release air bubbles.
Bake for 14 to 15 minutes or until the bottom is lightly golden brown.
Rest in the pan for 2 minutes, then turn the cake out onto a powdered sugar dusted tea towel. Remove parchment paper and roll the cake up in the towel into a log. Keep seam side down and cool completely, about 2 hours.
Beat butter and vanilla extract until creamy. Add powdered sugar and coffee creamer and mix on low until combined, then beat on high until light and fluffy. Scoop 1/2 cup of frosting into a piping bag fitted with a star tip.
Carefully unroll the cooled cake and spread the remaining frosting evenly over the surface. Roll the cake back up.
Pipe stars over the outside of the cake and top with patriotic sprinkles. Refrigerate for at least 2 hours before slicing and serving.