Preheat the oven to 425 degrees F. Place a half-sheet pan in the oven to heat.
Place a saucepan over a medium heat, then add the evaporated milk, processed cheese, 1 cup of the Cheddar, 1 cup of the Gruyere, the dry mustard, hot sauce and salt, then whisk until the cheeses are melted and the mixture is smooth, 2 to 3 minutes. Add the cooked pasta to the cheese sauce and stir to coat and combine.
In a small bowl, toss together the Parmesan with the remaining 1 1/2 cups Cheddar and 1 1/2 cups Gruyere.
Remove the sheet pan from the oven and carefully spray with the cooking spray. Pour the mac and cheese from the saucepan into the sheet pan and spread evenly.
Sprinkle the cheese mixture evenly over the top. Bake until the cheese topping is fully melted and the mixture is bubbly, 15 to 20 minutes.
Remove from the oven, then garnish with the basil and serve.