The custard, a versatile dessert sauce that's also great with fresh fruit, makes use of some of the extra egg yolks. For a fitting garnish, arrange a few chocolate-covered coffee beans around the cake.
To prepare cake, lightly spoon flour into a dry measuring cup; level with a knife. Combine flour, 3/4 cup sugar, and cinnamon, stirring with a whisk, and set aside. Combine espresso and hot water, stirring until espresso dissolves; set aside.
Place egg whites in a large bowl; beat with a mixer at high speed until foamy. Add cream of tartar and 1/4 teaspoon salt; beat until soft peaks form. Add 3/4 cup sugar, 2 tablespoons at a time, beating until stiff peaks form.
Beat in espresso mixture and vanilla extract. Sift 1/4 cup flour mixture over egg white mixture; fold in. Repeat procedure with remaining flour mixture, 1/4 cup at a time.
Spoon batter into an ungreased 10-inch tube pan, spreading evenly. Break air pockets by cutting through batter with a knife. Bake at 350° for 50 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 plate.
To prepare sauce, place egg yolks in a large bowl; set aside. Combine 1/2 cup sugar, cornstarch, and 1/8 teaspoon salt in a medium saucepan. Gradually add 1/2 cup milk, stirring with a whisk until smooth. Stir in remaining milk. Scrape seeds from vanilla bean into the milk mixture; add bean to mixture. Heat milk mixture over medium heat to a boil. Remove from heat; gradually add hot milk mixture to egg yolks, stirring constantly with a whisk.
Return milk mixture to pan. Cook mixture over medium heat until thick and bubbly (about 4 minutes), stirring constantly. Remove from heat. Spoon milk mixture into a bowl; place bowl in a large ice-filled bowl for 10 minutes or until milk mixture comes to room temperature, stirring occasionally. Remove bowl from ice; stir in liqueur. Cover and chill completely.
Remove and discard vanilla bean. Serve angel food cake with sauce, and sprinkle with toasted hazelnuts.