Combine eggs and sugar in a large Dutch oven; beat well. Add flour, stirring until smooth. Gradually stir in milk and whipping cream. Cook over medium heat, stirring constantly with a metal spoon, 40 minutes or until mixture thickens and coats the spoon. (If necessary during cooking procedure, beat mixture well with a wire whisk.) Remove from heat; stir in vanilla. Cool to room temperature; cover and chill thoroughly.