Step 1
Preheat oven to 350°. Lightly coat two 9″-diameter cake pans with nonstick vegetable oil spray and line each with a parchment paper round. Whisk 1¾ cups (219 g) all-purpose flour, 1 cup (200 g) granulated sugar, ½ cup rainbow sprinkles, 2 tsp. Diamond Crystal or 1¼ tsp. Morton kosher salt, 1½ tsp. baking powder, and ½ tsp. baking soda in a medium bowl to combine.
Step 2
Whisk 2 large eggs, ¾ cup sour cream, ⅔ cup vegetable oil, and 1 Tbsp. vanilla extract, and 2 Tbsp. water in a large bowl to combine. Add dry ingredients and fold with a rubber spatula just until no floury streaks remain (be careful not to overmix). Divide batter between prepared pans and smooth surface of each.
Step 3
Bake cakes until a tester inserted into the centers comes out clean, 20–25 minutes. Transfer pans to a wire rack and let cakes cool in pans 10 minutes. Turn cakes out onto rack and let cool completely. Wrap each layer tightly in plastic and freeze at least 1 hour.
Step 4
Let 2 pints strawberry ice cream and 2 pints vanilla ice cream set at room temperature 15 minutes to soften.
Step 5
Meanwhile, lightly coat a 9″-diameter springform pan with nonstick spray. Line inside of pan with 2 long strips of plastic wrap, running one in each direction, pressing into edges, and leaving at least 5″ overhang on all sides.
Step 6
Scrape softened strawberry ice cream into a large bowl (the edges will be slightly meltier than the centers). Mash and mix ice cream with clean spatula until spreadable and homogenous. Scrape into prepared pan and smooth into an even layer with spatula or a spoon. Top with a frozen cake and press down slightly on cake to adhere (this should eliminate any gaps, but don’t press too hard or the ice cream will come out the sides). Repeat process with vanilla ice cream in a clean large bowl and remaining cake. Bring plastic wrap overhanging up and over cake to enclose and freeze at least 12 hours.
Step 7
When ready to serve, remove ice cream cake from freezer and remove sides from pan. Peel back plastic wrap from top of cake and hold a platter upside down over cake; invert cake onto platter. Remove bottom of pan and peel off plastic wrap. Let cake sit at room temperature 5 minutes to soften slightly.
Step 8
Meanwhile, using an electric mixer on medium-high speed, beat ¾ cup heavy cream, 2 Tbsp. powdered sugar, a pinch of salt, and remaining ½ tsp. vanilla extract in a small bowl until soft peaks form (alternatively, whisk by hand).
Step 9
Run an offset spatula or bench scraper under hot water and wipe dry. Holding perpendicular to cake and pressing lightly, run around side to smooth and peel away excess ice cream (the motion is similar to crumb-coating a cake with frosting). Rinse spatula with hot water and dry with a kitchen towel after each stroke. Move quickly at this stage—if you fuss with it too much, the cake will start to melt. Don’t worry about smoothing the top as it will be covered with whipped cream.
Step 10
Mound whipped cream on top of cake and spread to the edges with a spoon or clean rubber spatula, making decorative swoops and swirls. Top with sprinkles.
Do Ahead: Cakes can be baked 1 week ahead; keep frozen. Cake (without whipped cream) can be assembled 3 days ahead; keep frozen. Assembled cake can be topped with whipped cream 1 day ahead; leave uncovered and freeze.