Have ready a fine-mesh strainer suspended over a medium glass bowl.

In the bowl of a food processor, process the chocolate until very fine. Add the butter and process just until incorporated.

In a 1 cup microwavable measure with a spout (or in a small saucepan over medium heat, stirring often), scald the milk (heat it to the boiling point; small bubbles will form around the periphery).

With the motor of the food processor running, pour the milk through the feed tube in a steady stream. Process for a few seconds until smooth, scraping down the sides of the bowl as needed. Press the ganache through the strainer and let it sit for 1 hour. Cover it with plastic wrap and cool for about 2 to 3 hours, until the mixture reaches a soft piping consistency (70° to 75°F/21° to 24°C).