Prepare an ice bath by filling the large bowl with ice and setting the medium bowl inside the larger bowl. Nestle the medium bowl into the ice so that at least three-quarters of the sides of the bowl are covered with ice. Set aside.
In a small bowl, sprinkle 2 1/4 teaspoons powdered gelatin over 1/4 cup cold water. Set aside for 5 minutes to bloom.
As the gelatin is blooming, transfer 12 ounces white chocolate to a food processor and pulse until very finely chopped. Place 3/4 cup heavy cream in a small saucepan, and bring just to a boil over medium-high heat. Be sure to watch the pot — cream tends to boil really quickly. Once the cream has been warmed, add the bloomed gelatin (from the 2nd step) and stir gently for 30 seconds to dissolve completely. Turn on your food processor and pour the mixture into the processor, continuing to process until the chocolate mixture becomes smooth.
Once the mixture is smooth and homogenous, transfer the white chocolate mixture into the medium bowl in the ice bath. Chill until the mixture is super thick, and almost gummy. The mixture should be thick enough to fall from a spoon in ribbons.
Use a handheld electric mixer to whip 1 1/2 cups heavy cream in a medium bowl. Continue beating until the cream starts to form heavy peaks — a spooned portion of the cream should hold its shape. Return to your white chocolate mixture and mix in the remaining 1/4 cup of the cream to loosen and thin out the mixture. Use a rubber spatula to fold the whipped cream (in the 6th step) into the white chocolate mixture until the two are fully incorporated — you should have a thick, heavy mousse that will hold its shape when piped. Chill in the refrigerator for an additional 10 to 15 minutes to set, before using immediately (if not using immediately, see baker's notes).