How to Make It
Prepare the Chocolate Sugar Cookie Dough: Beat butter and sugar with a heavy-duty electric stand mixer on medium-high speed until light and fluffy, about 3 minutes. Add eggs and vanilla. Beat on medium until combined, stopping to scrape down sides of bowl as needed.
Stir together flour, cocoa, baking powder, and salt in a medium bowl. With mixer running on low speed, add flour mixture to butter mixture, beating until just incorporated.
Shape dough into a disk, wrap tightly in plastic wrap, and chill at least 2 hours or up to 2 days.
Prepare the Cookies: Preheat oven to 350°F. Roll chilled dough to 1/4-inch thickness on a lightly floured surface. Cut with desired dog-shaped cutters, rerolling scraps as needed. If dough becomes warm and sticky, place in refrigerator for 15 minutes. Place cookies 2 inches apart on parchment paper-lined baking sheets, and chill 20 minutes.
Bake in preheated oven until tops of cookies are dry to the touch, about 10 minutes. Cool on baking sheets 2 minutes. Transfer to a wire rack to cool completely, about 30 minutes.
Prepare the Frosting: Beat powdered sugar, warm water, and meringue powder with a heavy-duty electric stand mixer on medium speed until smooth and glossy, about 2 minutes. Add vanilla extract and almond extract, and beat until combined, adding up to 2 Tbsp. water, 1 tsp. at a time, until desired consistency is reached. Divide frosting between 2 small bowls. Tint 1 bowl of frosting with desired amount of red food coloring gel; tint remaining bowl with desired amount of green food coloring gel.
Decorate cookies with icing and candy sprinkles. Let dry completely, about 1 hour.