Heat the oven to 375°F. Butter and flour a 9-inch springform pan, and set it aside.
Beat the butter and sugar together until light and fluffy, about two minutes. Add the eggs, one at a time, beating to incorporate after each addition, then add in the vanilla. Scrape down sides of bowl with a rubber spatula. Set aside.
Whisk together the flour, cornmeal, salt, baking powder, and nutmeg. Add the flour mixture to the batter in 3 parts, alternating with the buttermilk, starting and ending with flour. Make sure each addition is incorporated before adding the next, but don't over-beat it at the end. Spread the batter in the prepared pan and smooth the top.
Bake until the top is puffed and golden brown and a tester inserted in the center comes out clean, 30 to 35 minutes. Cool on a rack before serving warm or room temperature.