In a large mixing bowl, whisk together flour, baking powder, and salt. Set aside.
Using a stand mixer or handheld mixer, beat butter and sugar together until light and fluffy, about 2 minutes.
Add eggs one at a time, mixing between each addition. Add vanilla extract and almond extract and beat until evenly combined.
Add dry ingredients in three increments, mixing on low between each addition. Continue mixing on low until no dry spots remain (do not over mix).
Lightly dust a work surface with flour.
Working with about ⅓ of the dough at a time, roll it out to about ¼-inch thick. Use cookie cutters to cut the dough into shapes and transfer them to a lightly greased sheet pan (you can also line it with parchment paper or a Silpat baking mat), leaving space between each cookie.
Transfer the sheet pan(s) with cookies to the freezer for 15 minutes. (This will minimize spreading as the cookies bake.)
While the cookies chill, preheat oven to 375°F / 190°C.
When the oven is heated and the cookies are done chilling, transfer sheet pans with cookies directly to the oven and bake until the cookies are just set and show a hint of golden brown around the edges, 8 to 10 minutes (if cookies are frozen solid, they may take 3 to 5 minutes longer).
Transfer to a cooling rack and cool completely before decorating.
Make Icing: Pour water in the bowl of a standing mixer or a large mixer (if using a hand mixer). Gently swirl the water around to coat the sides of the bowl (this will help to prevent the dried ingredients from sticking).
Add meringue powder and powdered sugar all at once.
Start mixing on low, scraping down the bowl as needed, until everything is evenly combined.
Increase speed to medium-high and beat for 1 minute.
Continue mixing on medium-high in 30 second intervals, stopping to check the consistency after each interval. To check the consistency, use a spatula or spoon to scoop and drizzle some icing over the surface. Watch the design you drew as you count to 10. The icing is done when it takes 10 seconds for the surface of the icing to turn completely smooth.
Divide icing between bowls and stir in food coloring as desired. Transfer to piping bags. Icing can be refrigerated for up to 2 days or frozen for up to 2 months.
Make sure that cookies have cooled completely before using the frosting to decorate. Let decorated cookies sit at room temperature until the icing is fully set (this can take 1 to 4 hours, depending on the temperature and humidity of the room).
Store cookies in a well-sealed container at room temperature for up to 3 days.