Bring a large pot of salted water to boil.
Place a large Dutch oven over medium heat and add 4 tbsp. butter. Add the flour and whisk until smooth. (Whisk continuously and scrape bottom of pan to avoid scorching). Cook until pale golden brown and fragrant, about 6 minutes. Add mustard and paprika along with a pinch of garlic salt and whisk to combine.
Carefully whisk in the milk and cream until completely combined and smooth. Bring to a low simmer over high heat, then reduce heat to medium. Continue to simmer, stirring frequently then slowly add the white and sharp cheddar, fontina, and brie and whisk until smooth. Add the parsley, tarragon, and salt and whisk until combined. Reduce the heat to the lowest setting.
In the boiling water, cook the pasta for eight to ten minutes until al dente. Drain and transfer into the sauce. Stir to combine season with garlic salt, fold in the remaining butter and top with cheese.