Cook fettuccine in salted boiling water until al dente. Reserve 1/2 cup pasta water, then drain.
Season shrimp with salt, pepper, and paprika. Sear in 2 tablespoons butter over medium-high heat, 1–2 minutes per side, adding garlic in the last 30 seconds. Remove shrimp and set aside.
In the same skillet, melt remaining butter and cook garlic for 30 seconds. Add heavy cream and simmer gently.
Reduce heat to low and whisk in parmesan gradually until smooth. Season with salt, pepper, and nutmeg.
Add drained pasta to the sauce and toss to coat, adding reserved pasta water as needed. Fold in shrimp.
Garnish with parsley and serve immediately.