Adjust an oven rack to the middle position (and the other beneath it). Preheat the oven to 350°F. Use baking Pam or butter then flour two 8 by 2-inch round cake pans; line the bottoms with parchment paper circles.
In a medium bowl, whisk together the eggs and egg yolks, then whisk in the vanilla, sour cream, and buttermilk. Set aside.
In a bowl of a stand mixer fitted with a paddle, combine the flour, sugar, baking powder, baking soda, and salt on low speed. With the mixer still running on the lowest speed (e.g. "Stir"), add the butter one piece at a time, dropping another piece in every couple of seconds, then keep mixing until the mixture resembles coarse sand.
With the mixer still running on low, slowly add half the wet ingredients (1 cup worth). Stop to scrape down the bowl, then increase the speed to medium and beat until incorporated, about 30 seconds. Drop the speed back to low, and slowly add the rest of the wet ingredients, pausing occasionally to scrape down the bowl (sides and bottom) and beater. Mix until just combined, scrape down the bowl again, then increase the speed to medium and beat for 20 seconds (the batter may still look a little bumpy). Scrape down the sides and bottom of the bowl once more, then use a spatula to fold the batter a few times and check that there are no major lumps in the batter.
Divide the batter between the prepared pans (about 600-620 grams per pan) and gently smooth the tops with a spatula. Tap each pan gently on the counter twice to help pop any bubbles. Bake the cakes about 25-30 minutes, rotating the pans halfway through. Start checking for doneness around minute 20, but expect the cakes to take closer to 30 minutes. The cakes are done when the tops are golden brown, the sides pull slightly away from the pan, and a wooden skewer or toothpick inserted in the centers comes out clean.
Transfer the pans to a wire rack and let cool for 20-30 minutes. Turn the cakes out of the pans onto the rack, remove the parchment paper from the bottom, and let cool completely (about 90 more minutes). Once cool, the cakes can be frosted or wrapped in plastic and refrigerated overnight/frozen for future use.