In a large pot of water over high heat, cook the linguine pasta in salted water according to package instructions until al dente. Reserve ¾ cup hot pasta liquid and stir in a generous pinch of saffron threads. Set aside.
Add 1 tablespoon olive oil to a large hot pan over medium heat. Drop in a generous pinch of saffron and cook for a minute.
Season the shrimp with salt and black pepper. Add it to the hot skillet and cook 3 minutes or until shrimp has just turned pink. Toss with 1 large clove minced garlic. Remove from heat and set aside.
In another saucepan heat the butter and cream cheese, whisking until smooth. Add the saffron infused pasta liquid along with ½ cup heavy cream and whisk to combine.
Simmer the sauce on low 2-3 minutes until creamy. Transfer the saffron alfredo sauce to the skillet the shrimp is in and return to heat. Bring the shrimp mixture back to a simmer and scrape all the flavorful bits from the bottom of the frying pan.
Toss the creamy shrimp sauce with the linguine and serve with fresh chopped parsley or chives as a garnish.