2 1 / 2 cups (310 g) all-purpose flour 1 1 / 2 cups (300 g) granulated sugar 2 tsp baking powder 1 / 2 tsp baking soda 3 / 4 tsp fine salt 1 cup (240 ml) buttermilk, room temperature 1 / 2 cup (115 g) unsalted butter, melted and cooled 1 / 3 cup (80 ml) neutral oil (canola or vegetable) 3 large eggs, room temperature 2 tsp pure vanilla extract 1 / 2 cup (80 g) rainbow sprinkles (jimmies), plus extra for topping 1 cup (226 g) unsalted butter, softened (for frosting) 3 1 / 2 cups (420 g) powdered sugar (for frosting) 2 tsp pure vanilla extract (for frosting) 2–3 tbsp heavy cream or milk (for frosting) Pinch fine salt (for frosting)
Preheat oven to 350°F (175°C). Grease a 9x13-inch metal baking pan and line the bottom with parchment for easy removal. In a large bowl, whisk together flour, sugar, baking powder, baking soda, and salt. In a medium bowl, whisk buttermilk, melted cooled butter, oil, eggs, and vanilla until smooth. Pour wet ingredients into dry and whisk just until mostly smooth; a few small lumps are fine. Quickly fold in the sprinkles (jimmies hold their color best). Spread batter evenly in the prepared pan. Bake 28–34 minutes, or until the top springs back and a toothpick inserted in the center comes out clean. Cool the cake in the pan on a rack for 15 minutes, then remove (if lined) or leave in the pan; cool completely before frosting. Make the frosting: In a stand mixer or with a hand mixer, beat softened butter on medium-high until creamy and pale, about 2 minutes. Gradually mix in powdered sugar and a pinch of salt on low, then add vanilla and 2 tablespoons cream/milk. Beat on medium-high until fluffy, 2–3 minutes, adding the remaining tablespoon cream/milk if needed for a smooth, spreadable consistency. Spread frosting over the cooled cake and shower with extra sprinkles. Slice and serve. Storage: Cover and keep at room temperature up to 2 days, or refrigerate up to 5 days (bring to room temp before serving). Cake can be baked a day ahead; frosting can be made up to 3 days ahead and rewhipped.
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