Allow butter and eggs to stand at room temperature for 30 minutes. Meanwhile, grease and lightly flour two 8x1-1/2-inch round cake pans; set aside.
Preheat oven to 350 degrees F. In a large mixing bowl stir together flour, granulated sugar, brown sugar, baking powder, baking soda, and 1 teaspoon nutmeg. Add butter, eggs, milk, and vanilla. Beat with an electric mixer on low speed until combined. Beat on medium speed for 1 minute. Spoon batter into the prepared pans, spreading evenly.
Bake for 30 to 35 minutes or until a wooden toothpick inserted near the centers comes out clean. Cool cake layers in pans on wire racks for 10 minutes. Remove layers from pans; cool completely on wire racks.
Place one cake layer, bottom side up, on a serving plate. Spread the top with Brown Sugar Meringue Frosting. Top with second layer, top side up. Spread top with the remaining frosting, swirling to form high peaks. If desired, use a kitchen torch to brown peaks of frosting. If desired, garnish with chopped pecans and additional nutmeg.
Brown Sugar Meringue Frosting
In a 2 quart top of a double boiler combine brown sugar, water, egg white, and cream of tartar. Beat with an electric mixer on low speed for 30 seconds.
Place the pan over boiling water (upper pan shouldn't touch water). Cook, beating constantly with the electric mixer on high speed, for 10 to 13 minutes or until an instand read thermometer registers 160 degrees F. when inserted in the mixture, stopping beaters and quickly scraping sides of bowl. Remove pan from heat; add vanilla. Beat about 1 minute more or until mixture is fluffy and holds soft peaks. Frost cake; serve cake within 2 hours. Makes about 2 1/2 cups.