Preheat oven to 350°F. Generously grease a Bundt pan and set it aside.
In the bowl of a stand mixer fitted with the paddle attachment, combine 1 cup granulated sugar and 1/2 cup unsalted butter (melted). Beat on medium speed until combined and creamy, about 2 minutes.
Add 2 large eggs, one at a time, beating well after each addition.
Reduce mixer speed to medium-low. Add 3/4 cup buttermilk and either the seeds from 1 vanilla bean or 2 teaspoons vanilla extract; mix until evenly combined. (If using a vanilla bean: split it lengthwise and scrape the seeds with the back of a knife; discard the pod.)
With the mixer on low, add 2 cups cake flour, 2 teaspoons baking powder, and 1/2 teaspoon salt. Beat just until the batter is smooth and no large streaks of flour remain—do not overmix.
Pour the batter into the prepared Bundt pan and smooth the top. Bake for 35–45 minutes, until a toothpick inserted into the center comes out clean or with just a few crumbs attached.
Remove the cake from the oven and let it cool in the pan on a wire rack for about 10–15 minutes. Run a butter knife around the edges to loosen the cake, then invert the pan onto the wire rack and allow the cake to cool completely.
While the cake cools, make the glaze: sift 2 cups confectioners' sugar into a medium bowl. Add 3–4 tablespoons buttermilk and 1 1/2 teaspoons vanilla extract. Whisk until smooth. If the glaze is too thick, add more buttermilk 1 tablespoon at a time; if it is too thin, add more confectioners' sugar 2 tablespoons at a time. The glaze should be pourable but thick enough to hold some shape.
When the cake is completely cool, place it on a serving plate or keep it on the wire rack with a tray underneath. Pour the glaze over the top of the cake, letting it drip down the sides. If desired, sprinkle 1/2 cup rainbow sprinkles on top.
Notes
Notes
*You will cut the vanilla bean in half, then scrape the inside into the batter, or simply use vanilla extract.