Heat half-and-half in a heavy saucepan over low heat. Stir in chocolate morsels, marshmallows, and salt; cook over low heat, stirring constantly, until chocolate and marshmallows are melted. Remove from heat, and stir in vanilla extract. Cover and store in refrigerator up to 2 days, if desired. To serve warm, heat over low heat 5 minutes, stirring frequently.