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

In a food processor, process the white chocolate and bittersweet chocolate until very fine.

In a 2 cup or larger microwavable measure with a spout (or in a small saucepan over medium heat, stirring often), scald the cream (heat it to the boiling point; small bubbles will form around the periphery).

With the motor of the food processor running, pour the cream 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 let it cool for 2 to 3 hours, or until the mixture reaches soft frosting consistency (70° to 75°F/21° to 24°C).

The ganache keeps in an airtight container for 3 days at cool room temperature, 2 weeks refrigerated, or 6 months frozen. To restore to frosting consistency, defrost, if frozen, and reheat in a microwave with 3 second bursts, or in a double boiler set over hot, not simmering, water (do not let the bottom of the container touch the water), stirring gently to ensure that it does not overheat or incorporate any air.