- Preheat oven to 325℉. Grease three 8” round cake pans with cooking spray and line bottoms with parchment paper rounds.
- In a medium bowl whisk together flour, baking powder, and salt.
- In a large bowl with a hand mixer or a stand mixer fitted with the paddle attachment beat butter until smooth and creamy. Add 1½ cups sweetener and beat until very light and fluffy, about 5 minutes. Beat in vanilla.
- With mixer on low speed, beat in flour mixture in 3 parts alternating with milk in 2 parts.
- In a separate large bowl with clean beaters beat egg whites and cream of tartar or lemon juice on medium speed until soft peaks form. With mixer running, gradually add remaining ½ cup sweetener and beat until stiff peaks form (when you lift up the beaters and hold them sideways, the meringue should not droop).
- Fold ¼ of beaten egg whites into cake batter, then fold in remaining whites. When egg whites are almost completely incorporated, fold in sprinkles in a few quick strokes. Divide batter evenly among prepared pans, then spread it evenly with a small offset spatula.
- Bake, rotating pans in oven and switching oven racks, until a toothpick inserted in center of cakes comes out clean, 35-40 minutes. Cool cakes in pans for 10 minutes. Run a thin knife around the inside of cake pans and invert cakes onto a rack to cool completely.
- For the frosting, in a large bowl whisk to combine sweetener and tapioca starch. Blend in a high-speed blender in 2 batches until very fine and powdery, about 4 minutes. If needed, scrape down sides of blender a few times.
- In a large bowl with a hand mixer or a stand mixer fitted with the paddle attachment beat butter until smooth. Gradually add sweetener and beat until combined. Beat in vanilla and salt. Beat in cream a little at a time until frosting is a smooth, spreadable consistency. If too much liquid is added, frosting will start to separate. If this happens, add 1 tablespoon tapioca starch at a time, beating constantly, until frosting is smooth.
- On a serving plate or cake stand place one cake layer. Top with ⅓ of frosting and spread right to the edge of cake with an offset spatula. Top with second cake layer, then ⅓ of frosting, spreading it as above. Top with final cake layer, then remaining frosting, using spatula to make swirls in icing. Decorate with sprinkles.
- Make sure all ingredients are at room temperature (around 70℉).
- Prepare frosting and frost cake right before serving. Frosting stiffens as it sits.