Preheat oven to 325°.
To prepare cake, lightly spoon flour into a dry measuring cup; level with a knife. Combine flour and 3/4 cup granulated sugar, stirring with a whisk; set aside.
Place cream of tartar, salt, and egg whites in a large bowl; beat with a mixer at high speed until foamy. Add remaining 3/4 cup granulated sugar, 1 tablespoon at a time, beating until stiff peaks form. Beat in juice and 1/2 teaspoon vanilla. Sift flour mixture over egg white mixture, 1/4 cup at a time; fold in after each addition.
Spoon half of batter into an ungreased 10-inch tube pan, spreading evenly. Break air pockets by cutting through batter with a knife. Sift 2 tablespoons cocoa over remaining batter; fold in. Spoon cocoa batter evenly over top of vanilla batter; break air pockets by cutting through cocoa layer with a knife. Bake at 325° for 55 minutes or until cake springs back when lightly touched. Invert pan; cool completely. Loosen cake from sides of pan using a narrow metal spatula. Invert cake onto a plate.
To prepare glaze, place powdered sugar, cream cheese, milk, and 1 teaspoon vanilla in a medium bowl; beat with a mixer at medium speed until smooth. Drizzle half of glaze over cake.
Add 3/4 teaspoon cocoa to remaining glaze; stir well to combine. Drizzle cocoa glaze over cake. Refrigerate 5 minutes or until glaze is set. Garnish with strawberries, if desired.
Place leftover egg yolks in an airtight container, cover with a thin layer of water, and refrigerate for up to two days; use them to make custards, such as our Cinnamon Crème Anglaise.