Preheat the oven to 350°F and line baking sheets with parchment.
Cream butter and sugar until smooth, then mix in the egg and vanilla.
Add flour and combine thoroughly.
Knead dough and roll it out to about ⅝ inch thickness.
Cut rectangles and bake for 11–12 minutes.
Cool completely. For the icing, combine half the sugar with meringue powder, vanilla, and water; in another bowl, mix the remaining sugar, corn syrup, vanilla, and water.
Combine both icings and mix until smooth.
Add green coloring and transfer to a piping bag.
Outline and flood cookies, smoothing with a toothpick. Let dry for 12–16 hours.
For the chalk, melt white chocolate and pipe into straw segments.
Let set, then remove gently. Use the chalk to write on the cookies.