Preheat your oven to 350°F (175°C). Generously grease and flour a 10-cup bundt pan, ensuring every crevice is coated. For extra insurance against sticking, you can also use baking spray with flour.
In a large bowl, whisk together the flour, granulated sugar, baking powder, and salt. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment (or using a hand mixer and a large bowl), cream together the softened butter until light and fluffy. Beat in the eggs one at a time, ensuring each is fully incorporated before adding the next. Stir in the vanilla extract and the scraped seeds from the vanilla bean.
In a separate small bowl, whisk together the sour cream and milk.
Gradually add the dry ingredients to the wet ingredients, alternating with the sour cream mixture, beginning and ending with the dry ingredients. Mix on low speed until just combined. Be careful not to overmix.
Pour the batter evenly into the prepared bundt pan. Smooth the top with a spatula.
Bake for 50-60 minutes, or until a wooden skewer inserted into the center of the cake comes out clean. The cake should be golden brown and slightly pulled away from the sides of the pan.
Let the cake cool in the pan on a wire rack for 15-20 minutes before inverting it onto the wire rack to cool completely. Ensure the cake is entirely cool before frosting.
While the cake cools, prepare the frosting. In the clean bowl of your stand mixer (or using a hand mixer), beat together the softened cream cheese and softened butter until smooth and creamy. Gradually add the sifted powdered sugar, mixing on low speed until incorporated. Add the vanilla extract and 2 tablespoons of milk. Beat on medium-high speed until the frosting is light, fluffy, and spreadable. Add more milk, one tablespoon at a time, if needed to reach your desired consistency.
Once the cake is completely cool, generously spread or drizzle the cream cheese frosting over the top of the bundt cake, allowing it to drip down the sides. For an extra touch, you can sprinkle some colorful confetti or sprinkles over the frosting before it sets.