In a heavy saucepan, combine the first five ingredients. Cook over medium-low heat, stirring constantly, until the mixture is thick enough to coat a metal spoon and reaches at least 160 degrees F. Remove from the heat; cool quickly by setting pan in ice and stirring the mixture. Cover and refrigerate overnight or freeze immediately. When ready to freeze, pour custard and vanilla into the cylinder of an ice cream freezer. Freeze according to the manufacturer's directions.