Place a rack in the center of the oven; heat to 350°F. Butter or coat an 8-inch square baking pan with nonstick spray. Line the pan with a strip of parchment paper that hangs over two of the edges.
Make the Cake: In a large bowl, whisk the eggs and granulated sugar for about 1 minute, until pale and foamy. Add the sour cream, butter, nutmeg, vanilla, and salt. Whisk until smooth and emulsified.
Add the flour, baking powder, and baking soda. Whisk until well combined and smooth.
Pour the batter into the prepared pan and bake for 25 to 35 minutes, until puffed and golden, and a tester inserted into the center comes out clean. Set the pan on a wire rack to cool for about 15 minutes. Using the parchment overhang, lift the cake out of the pan and set on the wire rack to cool almost completely.
Finish the Cake: While the cake is just warm to the touch, brush the top with the butter and dust with the confectioners’ sugar. You should have a nice thick layer of confectioners’ sugar—more than you think might be necessary.
Do Ahead: The cake can be made 3 days ahead. Store, covered, at room temperature. The cake will absorb the sugar on top, so it might need a fresh dusting of confectioners’ sugar after the second day.