Heat oil in deep fryer or heavy skillet to 375°F.
Set up a dredging station with three bowls — 2 cups flour in the first one, beaten eggs and ½ cup milk in the second one and crushed Flamin’ Hot Cheetos in the third one.
Coat each cheese square and mozzarella stick in flour, submerge in egg wash and cover in Flamin' Hot Cheetos. Repeat this step a second time if necessary.
Deep fry for 45 seconds and drain on paper towels.
In a sauce pan, melt butter over medium heat and stir in ½ tablespoon flour. Add ¼ cup milk and reduce heat to low. Stir in shredded cheese slowly until melted.
Assemble sandwiches by placing one of your deep fried cheese squares on a plate and topping it with mozzarella sticks, meted Cheddar and finally the second deep fried cheese square.
