In a pot of salted boiling water, cook the pasta until fully cooked. Drain and set aside.
With the rack in the middle position, preheat the oven’s broiler. Butter an 8-cup (2 litre) baking dish or four 2-cup (500 ml) ramekins.
In a pot, melt the butter. Add the flour and spices and cook for 1 minute, stirring continuously. Add the evaporated milk and broth and bring to a boil, stirring with a whisk.
Remove from the heat and add 1 cup (100 g) of the cheddar, 1 cup (100 g) of the havarti and all of the Velveeta-style cheese. Stir until well incorporated. Add the pasta and cook just until heated through. Adjust the seasoning.
Spoon into the baking dish or ramekins. Sprinkle with the remaining cheese. Bake for 5 minutes or until the cheese has lightly browned.