In a medium bowl, simply whisk together the flour, cocoa powder, instant espresso powder, baking soda, and salt until well combined. Set this aside for a moment.
In a separate large bowl, using an electric mixer, beat the softened butter with both granulated and brown sugars on medium-high speed for 2-3 minutes until the mixture is light and fluffy.
Beat in the egg, vanilla extract, rum extract, and milk until everything is nicely combined and airy. Don't forget to scrape down the sides of the bowl!
Turn your mixer to low speed and gradually add the dry ingredients into the wet mixture, mixing just until a soft cookie dough forms. Cover the bowl with plastic wrap and pop it into the fridge for at least 2 hours, or even better, overnight (up to 3 days). This chilling step is super important for perfect cookies!
When ready to bake, preheat your oven to 350°F (175°C). Line two large baking sheets with parchment paper. If your dough has been chilling for a long time, let it sit at room temperature for 15-30 minutes to make it easier to scoop.
Using a medium cookie scoop (about 3 Tablespoons), drop scoops of the sticky dough onto the prepared baking sheets, leaving 2-3 inches between each cookie. Bake for 10-12 minutes, or until the edges look set and the tops are still slightly soft.
Let the baked cookies cool on the baking sheets for 5 minutes, then gently transfer them to a wire rack to cool down completely.
Once the cookies are totally cool, melt your white chocolate in a microwave-safe bowl (a tall liquid measuring cup works great) in 30-second bursts, stirring well after each, until it's smooth and melted. Dip half of each cookie into the melted white chocolate, then place them on a piece of parchment paper. Garnish immediately with 1-3 coffee beans for that classic look. Let the chocolate set at room temperature or speed it up with a few minutes in the freezer.