Whisk the flour, cocoa powder, baking soda, and salt together in a medium bowl. Set aside.

Using a hand mixer or a stand mixer fitted with paddle attachment, beat the butter, brown sugar, and granulated sugar together on medium speed until creamy, about 3 minutes. (Here’s a helpful tutorial if you need guidance on how to cream butter and sugar.) Add the egg and vanilla extract and mix on high until combined, about 1 minute. Scrape down the sides and bottom of the bowl as needed.

Pour the dry ingredients into the wet ingredients, add the milk and food coloring, and then mix on low speed until everything is combined. The dough will be sticky. If you want a more vibrant hue, beat in more food coloring a little at a time. Cover and chill the dough in the refrigerator for at least 2 hours (and up to 3 days). If chilling for longer than a few hours, allow dough to sit at room temperature for at least 15 minutes before rolling and baking because the dough will be quite hard.

Preheat oven to 350°F (177°C). Line large baking sheets with parchment paper or silicone baking mats. Set aside.

Scoop and roll cookie dough, about 1.5 Tablespoons of dough each. (A medium cookie scoop is helpful here.) Arrange on the baking sheet about 3 inches apart. Bake for 11–13 minutes or until the edges appear set. Centers will look very soft.

Remove cookies from the oven and cool for 5 minutes on the baking sheets. Transfer to a wire rack to cool completely.

In a microwave-safe bowl, melt the white chocolate in 15 second increments stopping and stirring after each until perfectly smooth. (Stir in 1 teaspoon vegetable oil if chocolate seems too thick for dipping.) Dip half of each cooled cookie into white chocolate and garnish white chocolate with sprinkles.

Allow chocolate to set completely at room temperature or in the refrigerator.

Cover and store leftover cookies at room temperature for up to 3 days or in the refrigerator for up to 1 week.