Bring a large pot of salted water to a boil and cook the fettuccine according to package instructions until al dente; drain and reserve a little pasta water if desired.
In a bowl, sprinkle the shrimp with 1 tablespoon Cajun seasoning and toss to coat evenly.
Sprinkle the 2 tablespoons flour over the seasoned shrimp and toss until each shrimp is lightly coated in flour.
Heat the butter and olive oil in a large deep skillet over medium-high heat until hot and shimmering.
Add the shrimp and cook about 2 minutes per side, until crisp and cooked through; transfer the shrimp to a plate and set aside.
Reduce heat to medium and pour the chicken broth and heavy cream into the same skillet, stirring to loosen any browned bits; season with additional Cajun seasoning and salt and pepper to taste.
Bring the sauce to a gentle boil, then whisk in the grated Parmesan until the sauce is smooth and slightly thickened.
Add the cooked fettuccine and the shrimp back to the skillet; toss to coat the pasta and shrimp in the sauce, adding a splash of reserved pasta water if needed to loosen the sauce.
Remove from heat, garnish with chopped parsley and extra Parmesan if desired, and serve immediately.
