Position a rack in the center of your oven and preheat to 350 degrees F. Butter two 9-inch round cake pans, line the bottoms with parchment rounds, and dust with flour, tapping out excess. Bring butter, eggs, and milk to room temperature - this takes about 30 minutes on the counter and makes all the difference for a smooth batter.

In a large bowl with a stand mixer fitted with the paddle attachment, beat the butter, granulated sugar, and scraped vanilla bean seeds on medium-high speed until pale and fluffy, about 4 minutes. Stop and scrape down the bowl twice - you want no gritty sugar at the bottom. The mixture should look almost like thick frosting and hold soft peaks.

Add the eggs one at a time, beating well after each addition until fully incorporated. If the batter looks slightly curdled, don't worry - it will come together in the next step. Scrape down the bowl after the second and fourth egg.

In a medium bowl, whisk together the flour, baking powder, and salt. With the mixer on low speed, add the dry ingredients in three additions alternating with the milk in two additions, beginning and ending with the flour. Mix just until the last streaks of flour disappear - overmixing develops gluten and makes a tough cake.

Divide the batter evenly between the prepared pans and smooth the tops with an offset spatula. Bake until the cakes spring back when lightly pressed in the center and a toothpick comes out clean, 30 to 35 minutes. The edges will be just pulling away from the pans. Cool in pans on a wire rack for 15 minutes, then turn out and cool completely, about 1 hour.

In a clean bowl, beat the butter and vanilla bean seeds on medium speed until creamy, about 2 minutes. Gradually add the powdered sugar on low speed until incorporated, then increase to medium-high and beat until fluffy, about 3 minutes. The frosting will look thick and slightly dry at this stage.

Add the heavy cream and salt, then beat on medium-high until the frosting is light, spreadable, and holds medium peaks, about 2 minutes more. Use immediately or cover with plastic wrap pressed directly on the surface for up to 4 hours at room temperature.

Place one cake layer on a serving plate. Spread about 1 cup of buttercream evenly over the top. Place the second layer on top, flat side up. Apply a thin coat of frosting all over the cake to seal in the crumbs, then chill for 15 minutes. Finish with the remaining frosting, swirling decoratively. The cake keeps at room temperature for 2 days or refrigerated for 5 days.