In a large mixing bowl, whisk together the melted butter and sugars until combined. Add the egg, red food coloring, vinegar and vanilla, and whisk until glossy-looking.

Sift the baking soda, baking powder, salt and cocoa powder over top of the mixture. Whisk until completely incorporated, ensuring there are no lumps.

Add the flour and fold in with a rubber spatula until the last streaks of white disappear.

Chill, covered, in the refrigerator for 30 minutes. Then measure out about 14 dough balls using a 1.5 ounce scoop. Cover the balls and chill them again for an hour.

Preheat the oven to 350°F. When the oven is preheated, place 7 dough balls on a parchment-lined half sheet tray.

Bake for 8-10 minutes on the middle rack. They should be set on the edges but still slightly underdone in the center. Allow to cool for a minute or two on their tray, then transfer to a wire rack to cool completely. Repeat with the remaining dough.

Prepare the glaze. For the white chocolate rum butter glaze: Set a large heat-safe bowl on top of a saucepan or pot filled with an inch of water; the bottom of the bowl should not touch the water. Bring the water to a gentle simmer over low heat. Add the butter and white chocolate to the bowl and allow to melt, stirring occasionally.

Once the mixture is melted and totally smooth, transfer the bowl to your work surface and beat in the powdered sugar as well as you can (you may not get it totally combined.) Mix together 1 tablespoon of the simmering water and the rum in a small bowl, then drizzle that into the butter and white chocolate mixture and continue beating until it comes together in a thick glaze.

Dip one of the cooled cookies to see if the glaze is thick enough. If it runs off, wait a minute or two, stir well and try again. It should be thick and opaque, but don’t wait too long because it will set up quickly. Dip the cookies about one-third into the glaze then place back on the parchment-lined sheet to set completely. Top the glaze with sprinkles, if desired.