Nutmeg is the secret ingredient that makes this playful Bundt taste just like a cake doughnut. (Be sure to use freshly grated nutmeg--you'll really notice the difference in flavor.)
Position a rack in the lower third of the oven. Preheat oven to 325°. Generously coat a 12- to 15-cup fluted tube pan with cooking spray; invert pan on a paper towel to allow any excess to drip out.
In a medium bowl, whisk together flour, baking powder, nutmeg, salt and baking soda.
In a large bowl, beat softened butter with a mixer on medium-high until creamy. Add granulated sugar and vanilla; beat until light and fluffy, about 3 minutes. Beat in eggs, one at a time, until combined. Reduce mixer speed to low. Beat in flour mixture and buttermilk in five alternating additions, beginning and ending with flour mixture. The batter will be very thick.
Spoon batter into prepared pan and smooth the top. Bake until cake is golden and a toothpick inserted in center comes out clean, about 1 hour. Cool in pan on a wire rack 15 minutes.
To coat the cake, line a baking sheet with wax paper. Place powdered sugar in a fine-mesh sieve placed over a medium bowl. Use a thin knife to gently loosen cake from pan but leave cake in pan.
Using a pastry brush, very lightly brush cake with melted butter, just enough to moisten but not saturate the surface. (Too much butter will make the sugar dissolve.) Generously dust cake with a thick layer of powdered sugar, tapping the side of the sieve. Let rest 5 minutes. Carefully invert cake onto prepared baking sheet; remove pan. Very lightly brush cake all over with remaining melted butter. Thickly dust cake with powdered sugar. Tilt and rotate pan while you dust, holding the parchment with your thumb so the cake doesn't slide. Keep working until the entire cake is covered with sugar. Cool completely on baking sheet.
When cool, touch up cake with additional powdered sugar as needed. Use a thin spatula and your hands to gently lift and transfer cake to a serving platter.