To make the cake batter, whisk the flour, salt, baking powder, and nutmeg together in a medium bowl.
Beat the 1 stick of butter, the remaining 3/4 cup sugar and the vanilla with an electric mixer on low speed until combined well, about 1 minute.
Increase speed to medium high and beat for 4 to 5 minutes more until fluffy and light, stopping to scrape the bowl and beater once.
Beat in the eggs one at a time, beating well after each. The batter will look curdled. That’s okay.
Scrape the bowl and stir in half the dry ingredients.
Stir in the milk, then the remaining dry ingredients.
The batter will be thick. Spread it evenly over the peaches.