COMBINE cookie mix, butter and egg in medium bowl until soft dough forms. Divide dough in half.
STIR orange peel into one half of dough. Knead red and yellow food color into remaining dough until evenly colored. Divide both dough halves in half again to make 4 parts. Roll each one between sheets of wax paper into 10 x 8-inch rectangles. Place on top of each other on cookie sheet. Chill 15 minutes.
REMOVE one sheet of wax paper from sheets of dough. Turn one light orange layer upside down onto one dark orange layer aligning corners. Remove other sheet of wax paper from light layer. Beginning on long side, roll up dough using the wax paper to make a rounded log. Roll in orange sprinkles to completely cover the outside. Wrap wax paper around log. Repeat with remaining 2 sheets of dough. Freeze 1 hour.
HEAT oven to 375°F. Cut logs into 1/4-inch slices. Place on cookie sheet. Bake 7 to 9 minutes or until just lightly browned. Cool on cookie sheet 2 minutes. Transfer to wire rack to cool completely. Spread frosting on bottom side of half the cookies. Place another cookie, bottom side down, on top of the frosting to make sandwich cookies.
TIP Keep second log in freezer until ready to bake. Return to freezer as needed to make slicing easier.