Instructions

1. Place 15 tablespoons of the unsalted butter in the bowl of a stand mixer (or large bowl if using an electric hand mixer). Place 3 large eggs and 3/4 cup sour cream on the counter. Let everything sit at room temperature until the butter is softened.
2. Arrange a rack in the middle of the oven and heat the oven to 350°F. Meanwhile, melt the remaining 1 tablespoon unsalted butter in the microwave or on the stovetop. Add 1 tablespoon of the all-purpose or cake flour to the butter and whisk until a smooth paste forms. Brush a 10-cup (around 9-inch) Bundt cake pan with all of the paste, making sure to brush the tube.
3. Place the remaining 2 1/2 cups all-purpose or cake flour, 1 1/2 teaspoons baking powder, and 1/2 teaspoon baking soda in a large bowl and whisk to combine. If using a vanilla bean, split in half lengthwise. Scrape the seeds into a small bowl (save the pod for making vanilla extract), add 1 1/2 cups granulated sugar, and rub together with your fingers until the seeds are evenly distributed in the sugar.
4. Add 3/4 teaspoon kosher salt to the bowl of butter. Beat on medium speed with the paddle attachment for 30 seconds. With the mixer still running, gradually beat in the sugar and beat until combined, about 1 minute. Stop the mixer and scrape down the sides of the bowl.
5. Add the vanilla extract: 2 teaspoons if also using vanilla seeds, or 5 teaspoons if you are not using vanilla seeds. Beat on medium-high speed, scraping down the sides of the bowl halfway through, until lightened in color and fluffy, about 5 minutes total. Scrape down the sides of the bowl again.
6. Turn the mixer on to medium speed. Gradually add the eggs one at a time, waiting until each one is incorporated before beating in the next. With the mixer on the lowest speed, beat in half of the flour mixture until just combined. Add the sour cream and beat until just combined. Add the remaining flour and beat until just combined.
7. Transfer the batter into the Bundt pan and smooth the top. Pick up the pan and gently tap on the work surface a few times to remove any air bubbles.
8. Bake until a tester inserted into the cake comes out clean or with only a few moist crumbs, the cake bounces back when lightly pressed, and the top is golden-brown, 45 to 50 minutes. Place the Bundt pan on a wire rack and let cool for 30 minutes. Flip the cake out onto the rack and let cool completely, about 1 hour more.
9. Place 1 cup powdered sugar, 2 tablespoons milk, and 1 pinch kosher salt in a small bowl and whisk until smooth. Spoon evenly over the cake, letting it drip down the sides. Let sit until set, about 15 minutes.