COOKIES: Combine flour, corn starch and powdered sugar in medium bowl; set aside. Beat butter in large bowl with mixer at medium speed until smooth. Add flour mixture, lemon and vanilla; beat until well blended. Dough should gather to form a ball. Add 1 to 2 tablespoons additional flour if needed.
Refrigerate dough 15 minutes or until easy to handle. Preheat oven to 350°F.
Shape dough into 1½-inch balls; elongate to form egg shape (see TIP below). Place 1½ inches apart on ungreased baking sheets. Flatten slightly with floured fingers. Chill unbaked cookies 5 to 10 minutes prior to baking.
Bake at 350°F for 10 to 12 minutes or until edges are lightly browned. Remove; cool completely on wire racks. Decorate with icing (recipe follows below); store in tightly covered container.
NOTE: Dough can be made and frozen up to one month ahead. Remove dough from freezer and refrigerate to thaw 24 to 48 hours before baking.
TIP: Egg-shaped cookies can be formed by covering a medium-sized, deep-bowled, oval-shaped spoon with plastic film and pressing dough into it: then invert onto cookie sheet. Chilled dough can also be rolled and cut with cookie cutters.
ICING: Combine powdered sugar, butter and enough milk to achieve a smooth, spreadable consistency in a mixing bowl. Divide icing into small bowls; one for each colour. Add food colouring; stir until uniformly blended. Icing can be spread onto cooled cookies using a spatula or transfer icing to a resealable plastic bag. Seal bag and snip bottom corner of bag; squeeze icing out to make patterns.