In a stand mixer fitted with a paddle attachment, beat butter until fluffy in a large bowl. Add white sugar and powdered sugar for about 3 minutes. The texture should be light in color and fluffy.

Beat in the egg and vanilla extract.

Combine the flour, cornstarch, and salt in a bowl. 

With the mixer on low speed, slowly add the dry ingredients to the sugar mixture. Stir just until combined; the dough will be soft.

Divide the dough in half and shape it into two 8-inch round discs. Cover each disc with plastic wrap and chill the dough for 2 hours.

Working with one disc at a time, place the chilled dough on a lightly floured surface and roll it with a rolling pin until it is ¼ inches thick.

Preheat the oven to 350ºF and line cookie sheets with parchment paper.

Press the stamp into the dough. If you're using a plunger-style stamp, stamp the cookie first and then use the cutter to create a clean cut. Reroll any dough scraps and continue stamping cookies until no dough remains, being careful not to overwork the shortbread dough. Remember to dip the cookie stamps in flour and tap off any excess after each stamp. 

Place the stamped and cut-out cookies on the prepared baking sheet and refrigerate them for about 20 minutes while the oven preheats. Repeat the process with the second dough disc.

Bake one cookie sheet at a time for 8 to 10 minutes , or until the edges are set. Let the cookies cool on the pan for 5 minutes before transferring them to a wire rack to cool completely before adding sugar.

After the cookies have cooled, add water to a small bowl, dip a cake decorating brush into it, and use it to paint the stamped cookie where you want the colored sugar to go on top of the cookie. While the cookie is still wet, sprinkle sugar onto it and allow it to dry. Then, lightly brush away the excess sugar.