Beat cream cheese and butter at medium speed with an electric mixer until creamy. Gradually add powdered sugar, beating until light and fluffy. Stir in vanilla extract.
Chocolate Glaze: Melt 1 (12-ounce) package semisweet chocolate morsels and 1/2 cup whipping cream in a 2-quart microwave-safe bowl at MEDIUM (50% power) 2 1/2 to 3 minutes or until chocolate begins to melt. Whisk until chocolate melts and mixture is smooth. Makes about 2 cups. Prep: 5 min.
Vanilla Glaze: Stir together 1 (16-ounce) package powdered sugar, 5 tablespoons milk, and 2 teaspoons vanilla extract just until powdered sugar is moistened and mixture is smooth. Add an additional tablespoon of milk, if needed. Use immediately. Makes about 1 1/2 cups. Prep: 5 min.
Note: We kept this glaze very thick so that it wouldn't drip all the way down the sides of the Fluted Chocolate-Red Velvet Cakes, but feel free to make it a little thinner if you'd like to drizzle it over other cakes.