Preheat oven to 350°; grease and lightly flour a 12-cup Bundt pan.
Measure the flour, baking powder, salt, and nutmeg into a bowl; sift or whisk to combine.
Using a stand mixer with the paddle attachment, beat the butter and sugar on med-high speed until the mixture is very light in color--almost white--and the texture is fluffy, about 7 minutes; scrape down the sides of the bowl a few times during the process.
Combine the egg whites and vanilla in a liquid measuring cup; with the mixer on medium speed, add the egg whites slowly (about 1/4 cup at a time), completely incorporating each before adding the next; scrape bowl as needed.
Note--to me, the author makes the next steps more complicated in her description; here is what I do when adding the dry and wet ingredients-- add flour mixture alternately with milk, beginning and ending with flour mixture (flour, milk, flour, milk, flour).
Author's instructions--Decrease mixer speed to low; add 1/3 of the dry ingredients to the mixer and incorporate on low speed, then increase to medium speed.
Add 1 cup of the milk and mix briefly to incorporate; reduce speed to low again, add half the remaining dry ingredients, and mix to incorporate, then increase the speed to medium and beat for 1 minute.
Repeat with the remaining 1 cup milk and the remaining dry ingredients, but stop mixing just before the flour is fully incorporated.
Finish the mixing by hand, using a sturdy spatula and being sure to scrape up from the bottom of the bowl.
Pour the batter into the prepared pan; bake for 45 minutes, then rotate the pan, lower oven temperature to 325°, and bake for 30 minutes more.
It's ready when the sides pull away from the pan slightly and it springs back when pressed lightly in the center; the top will probably split; use a cake tester to check for doneness.
Make the glaze while the cake is in the oven--measure the powdered sugar, cream, and vanilla into a small bowl and whisk until smooth.
Let the cake cool for 15 minutes before turning it out.
Whisk the glaze again until completely smooth, then use it immediately.
Saturate the cake completely, using a pastry brush to coat the entire surface.
Apply the entire amount of glaze; it will be enough for several coats.