Make the mousse first, so it has time to chill. Or better yet, make this mousse in advance! It can be made 1-2 days ahead of time.
Place a large mixing bowl and hand mixer beaters or the bowl of a stand mixer and whisk attachment in the freezer. This makes it easier and quicker to whip up the whipped cream for the mousse.
Melt 1/2 cup of dark chocolate chips in a medium-sized, heat-proof bowl. Heat in 20-30 second increments in the microwave, stirring after each interval until the chocolate is completely melted and smooth. You can also use a double boiler if you don't have a microwave.
In a small bowl, whisk together 1/3 cup of warm water and 1/4 cup of dark cocoa powder. Pour into the melted dark chocolate and whisk together until smooth. The mixture should be somewhat thick. Set aside.
Add 3/4 cup of white chocolate chips and 1/3 cup of heavy cream to a medium-sized, heat-proof bowl. Heat for 45-60 seconds in the microwave, then let the mixture sit for a minute. Stir until combined with a rubber spatula. The white chocolate should be completely melted, and the mixture should be smooth. You can also use a double boiler if you don't have a microwave. Set aside.
Then pour 2 cups of heavy cream, 1/4 cup of powdered sugar, 2 tsp of vanilla extract or vanilla bean paste, and 1/2 tsp of fine salt into a large bowl, or the bowl of a stand mixer fit with a whisk attachment.
Mix on medium-high speed until the whipped cream starts to gather in the whisk attachment and you can see texture around the edges of the bowl. The whipped cream should be thick and able to keep its shape. This usually takes about 2 1/2 to 3 minutes in my stand mixer.
Scoop half of the whipped cream into a separate bowl, and mix in the chocolate/cocoa/water mixture using a rubber spatula. Use the spatula to swoop around the sides of the bowl and pull through the center until the ingredients are fully combined. Be careful not to over-mix the mousse, or it will become deflated and lose its structure.
Pour the melted white chocolate/heavy cream mixture into the remaining whipped cream and fold together using a rubber spatula. At this point, the white chocolate mixture should have cooled down a bit and should still be fluid, but not hot to the touch. Use the spatula to swoop around the sides of the bowl and pull through the center. Be careful not to over-mix the mousse, or it will become deflated and lose its structure.
Cover both bowls of mousse with plastic wrap or scoop each mousse into its own piping bag and chill in the refrigerator for at least 2 hours.