Bring a large pot of salted water to a boil and cook the fettuccine according to package directions until al dente; drain and set aside.
Pat the shrimp dry. In a bowl, sprinkle 1 tablespoon Cajun seasoning over the shrimp, toss to coat, then add the flour and toss again so each shrimp is lightly coated.
Heat the butter and olive oil in a large deep skillet over medium-high heat until the butter is melted and shimmering.
Add the shrimp in a single layer and cook about 2 minutes per side, until crisp and opaque; remove the shrimp to a plate and reserve.
In the same skillet, pour in the chicken broth and heavy cream; season with additional Cajun seasoning if desired and salt and pepper to taste, then bring to a simmer.
Whisk in the grated Parmesan until the sauce is smooth and slightly thickened.
Add the cooked fettuccine and shrimp back to the skillet and toss gently to coat in the sauce and heat through.
Transfer to plates and garnish with chopped parsley and additional Parmesan if desired.