Oh you don't need to stablize before freezing...
I haven't made this more than a few days in advance, but if Steve says whipped cream keeps a long time, I don't see why this whole thing wouldn't too. I'd just make sure to wrap well so it doesn't pick up "freezer taste" or plan to add the whipped cream layer the night before serving so it has plenty of time to freeze up.
Please note though - I do not recommend the brownies as written. Every time I've used them the cake is incredibly difficult to cut and I nearly punched knife holes in my pan doing it. I now use the Supernatural brownies recipe for the batter to make the base for this. I cut the amount in half, then follow the directions in the Dulce de Leche Ice Cream Cake. Comes out great.
>>Make sure you cut this recipe in half for the ice cream cake!
Supernatural Brownies
by Nick Malgieri
2 sticks (1/2 pound) unsalted butter
8 ounces bittersweet or semisweet chocolate, cut into 1/4-inch pieces
4 large eggs
1/2 teaspoon salt
1 cup granulated sugar
1 cup firmly packed dark brown sugar
2 teaspoons vanilla extract
1 cup all-purpose flour
One 13x9x2-inch pan, buttered and lined with buttered parchment or foil
1. Set the rack in the middle of the oven and preheat to 350 degrees.
2. Bring a saucepan of water to a boil and turn off heat. Combine butter and chocolate in a heat proof bowl and set over pan of water. Stir occasionally until melted.
3. Whisk eggs together in a large bowl, then whisk in the salt, sugars, and vanilla. Stir in the chocolate and butter mixture, then fold in the flour.
4. Pour batter into prepared pan and spread evenly. Bake for about 45 minutes, until top has formed a shiny crust and batter is moderately firm. Cool in pan on a rack. Wrap pan in plastic wrap and keep at room temperature or refrigerated until the next day.