Position a rack in the center of the oven and heat the oven to 350°F. Butter a 12-cup Bundt pan, dust the pan with flour, and tap out the excess. In a small bowl, whisk together the flour, baking powder, and salt until evenly combined.
In the bowl of a stand mixer fitted with the paddle attachment, beat the butter and the sugar at medium speed until light and fluffy, about 2 minutes.
On low speed, beat in the yolks until smooth. Stop the mixer and scrape the bowl and the paddle. With the mixer running on medium-low speed, add the whole eggs, one at a time, mixing for at least 20 seconds after each addition. Stop the mixer and scrape the bowl and paddle again.
With the mixer running on the lowest speed, add half of the flour mixture and mix just to combine, add the milk and mix until combined, and then add the remaining flour mixture and mix just until combined.
Scrape the bowl one last time, add the vanilla extract, and mix at medium speed until the batter is smooth and fluffy, 20 to 30 seconds.
Scrape the batter into the prepared pan and spread it evenly. Run a knife through the batter and tap the pan against the counter to dislodge trapped air. Bake until golden brown and a toothpick inserted in the center comes out with only moist crumbs clinging to it, 45 to 55 minutes.
Cool in the pan for 10 to 15 minutes and then invert onto a wire rack to cool completely. The cake will keep at room temperature for 3 days.