Line a baking sheet with parchment paper.

In the bowl of a stand mixer fitted with the paddle attachment, beat butter and sugars at medium speed until fluffy, 3 to 4 minutes, stopping to scrape sides of bowl. Add egg, beating well. Beat in food coloring, vinegar, and extracts.

In a medium bowl, whisk together flour, cocoa, baking powder, salt, and baking soda. With mixer on low speed, gradually add flour mixture to butter mixture, beating until combined. Using a 1½-tablespoon spring-loaded scoop, scoop dough, and place on prepared pan. Cover and refrigerate for at least 1 hour.

Preheat oven to 350°F (180°C). Line 2 baking sheets with parchment paper. Place chilled dough at least 2 inches apart on prepared pans.

Bake until cookies look dry and edges are set, 12 to 14 minutes. Let cool on pans for 5 minutes. Remove from pans, and let cool completely on a wire rack.

In a small microwave-safe bowl, heat white chocolate on high in 30-second intervals, stirring between each, until melted and smooth. Dip cookies halfway in melted white chocolate, and transfer to a sheet of parchment paper. Sprinkle with crushed peppermints, if desired. Let set before serving.