Preheat the oven to 350°F and set aside an ungreased 9-inch tube pan. Sift the cake flour 4-5 times into a medium bowl to aerate it. Add 3/4 cup of sugar and the rainbow sprinkles to the sifted flour. Use a fork to thoroughly incorporate the ingredients. Sifting multiple times is important for the fluffy texture of angel food cake.
Place the 12 large egg whites (room temperature) in the bowl of a stand mixer. Add the pinch of cream of tartar, 1 teaspoon vanilla extract, and 1/8 teaspoon salt. Beat on medium speed until frothy, about 2 minutes. Measure out 3/4 cup of sugar and gradually add it to the egg whites, sprinkling in 1 tablespoon at a time and counting to 10 before each addition. Continue mixing until the mixture forms shiny, stiff peaks.
Gently fold one third of the flour mixture (from Step 1) into the stiff meringue (from Step 2). Once partly incorporated, repeat with the remaining flour mixture in two more additions, being careful not to deflate the meringue. Spoon the finished batter into the prepared tube pan and smooth the top. Gently bang the pan on the counter once to release any large air pockets. Bake for 45-50 minutes, or until a wooden skewer inserted into the center of the cake comes out clean.
Remove the cake from the oven and immediately turn it upside down to prevent it from sinking as it cools. Allow the cake to cool completely in the pan before attempting to remove it. I like to run a thin knife around the edge of the pan for easy release once it’s fully cooled.
Shortly before serving (about 30-60 minutes in advance), place the 6 large egg whites and 1 1/4 cups sugar in the bowl of a stand mixer. Use a hand whisk to combine the two. Set the bowl over a pot of simmering water, ensuring that the water does not touch the bottom of the bowl. Constantly whisk the mixture until the sugar has dissolved and the mixture is too hot to touch. Remove the bowl from the heat and attach it to the stand mixer. Whip with the whisk attachment on medium-high speed until the meringue has cooled, doubled in size, and is light and fluffy. Once cooled, add 3/4 teaspoon vanilla extract and 1/2 teaspoon kosher salt, whipping briefly to incorporate. For an extra-fluffy frosting, I sometimes whip a minute or two longer until it forms soft but stable peaks.
Frost the top, sides, and inside of the cooled angel food cake with the marshmallow frosting from Step 5, using a spatula to create swoops and peaks. Use a kitchen torch to lightly torch the frosting for a beautiful toasted effect. If you don’t have a torch, you can place the cake under your oven’s broiler and watch carefully, checking every 2 minutes until the frosting is golden. I love finishing this step with a few extra sprinkles for a festive touch.