Combine evaporated milk, flour, salt, pepper, and nutmeg in a saucepan, stirring with a whisk until smooth. Bring to a boil over medium-high heat; cook 1 minute, stirring constantly. Remove from heat. Add mayonnaise, next 4 ingredients (through soup), and 1/2 cup cheese, stirring until well combined. Add mayonnaise mixture to broccoli mixture; stir gently until combined.