Bring a pot of water to a boil. Add a spoonful of kosher salt and cook the pasta in the water 2 minutes less than the package directions. Scoop out ~1 1/2 cups of the water and drain the pasta.
Put the pot back on the heat, bring it down to low, and add the butter. Add 3 tablespoons of the flour and whisk for 1 minute.
Add one cup of milk and whisk vigorously until it is bubbly and thick. Add the remaining milk and bring to a simmer. Add the spices - mustard, paprika, cayenne, salt, and pepper.
Take the pot off the heat and let it cool until it's under 180F when checked with a thermometer.
Mix together the shredded cheeses with the remaining tablespoon of flour. Add cheese by the handful to the hot milk while whisking constantly.
Once you add the last handful, add the pasta back to the pot with 1 cup of the reserved water. Bring to a simmer, and cook, stirring frequently, for 3-4 minutes, until the sauce is thick and creamy and the pasta is cooked through.