Preheat the oven to 350°F (180°C). Grease two 8-inch springform cake pans and set aside.
In a large bowl, whisk together the flour, sugar, baking soda, and salt until evenly combined.
Add the vanilla extract, vinegar, vegetable oil (1/2 cup plus 2 tablespoons), and water to the dry ingredients and mix until a thick, smooth batter forms.
Gently fold the sprinkles (1/4 cup rainbow jimmies) into the batter until evenly distributed; avoid overmixing to prevent color bleed.
Divide the batter evenly between the prepared pans and smooth the tops. Bake for 27–30 minutes, or until a skewer inserted into the center comes out clean.
Remove the cakes from the oven and let them cool completely in the pans, then release from the springform pans.
If desired, use a wet knife to slice each cake horizontally to create four thin layers in total.
Place one cake layer on a serving plate, spread with frosting, and repeat with remaining layers to build a four-layer cake. Cover the exterior with the remaining frosting.
Let the assembled cake sit 30 minutes before serving.