Start by placing the chocolate-covered butter cookies in a food processor. Pulse until they become fine crumbs, resembling sand. In a mixing bowl, combine these crumbs with the rich Irish cream liqueur. Mix well until the crumbs are evenly moistened.

Next, add the mascarpone cheese to the cookie mixture. Using a spatula or hand mixer, blend until the ingredients form a smooth, cohesive mixture. Ensure there are no lumps.

Take a cookie scoop or your hands to form small balls, about one inch in diameter. Place each formed ball on a parchment-lined baking tray and freeze for at least 45 minutes.

While the cheesecake balls are chilling, prepare the coating. Fill a double boiler with water and place it over medium heat. Add the chopped white chocolate, stirring until it melts and becomes smooth.

With the cheesecake balls now firm, dip each ball into the melted white chocolate. Use a fork to let the excess chocolate drip off, then place on the parchment-lined tray. Refrigerate for at least one hour.

Melt the dark chocolate using the double boiler method. Once melted, drizzle the dark chocolate over the white chocolate-coated cheesecake balls. Allow the drizzled chocolate to set for at least 30 minutes before serving.