In a large bowl, beat the butter, sugar, sour cream, egg and vanilla on medium speed of an electric mixer until blended. Beat in the flour until well mixed.
Divide the dough in half. Mix food coloring into one half of the dough. Shape each dough into a flattened rectangle and wrap each in plastic wrap. Refrigerate for 2 hours or until the dough is firm enough to roll.
Cut 2 sheets of parchment paper 18 inches long and sprinkle with flour. On the floured parchment, roll each rectangle of dough into a 15x8-inch rectangle. Using the parchment to lift and flip the dough, place the red dough on top of the white dough and remove the top parchment. Gently press the doughs together. Using the bottom parchment to guide, roll up, jelly-roll fashion, starting with the 15-inch side. Cut the log crosswise in half (if the dough becomes too soft, return to the refrigerator for 30 minutes).
Place 2 tablespoons of the sprinkles on a piece of plastic wrap. Roll one log in sprinkles, pressing as you coat, to cover the outside of the log. Wrap the log in plastic wrap. Repeat with the remaining log. Refrigerate at least 4 hours until firm.
Heat the oven to 375 degrees. With a sharp knife, cut the log into 1/4-inch slices. Place 1 inch apart on ungreased cookie sheets. Bake for 7 to 9 minutes or until set. Cool for 2 minutes on the cookie sheet. Remove the cookies to a cooling rack to cool completely.