Blend butter and sugar until creamy. Add one egg and vanilla. Add the remaining ingredients and mix until well combined. Split the dough into thirds. Color 1/3 red and 1/3 green. Wrap all dough in plastic and chill for 30 minutes. After the dough has chilled, roll each color of dough in a rectangle 5" x13" (Use perfection strips for perfect thickness). Whisk one egg. Lightly brush the egg on top of the red dough. Place the green layer directly on top of the red layer. Lightly brush the green layer and place the white layer on top. Roll into a tight log. Wrap the log in plastic wrap and chill for 8 hours, or overnight. After chilling, cut the log into ¼ inch slices and arrange 1" apart on a lightly greased cookie sheet. Gently press cookie sticks into the bottom of the cookie, twisting to ensure sticks reach 3/4 of the cookie. Bake 8 to 10 minutes or until lightly browned.
For bouquet: Melt one pound candy coating. Add 2/3 cup corn syrup. Stir until blended thoroughly. Wrap in plastic wrap for several hours. Line mug with plastic wrap. Knead candy clay and place in the bottom of mug. Arrange lollipop cookies. Cover candy clay with jelly beans or other candies.