Season the chicken breast pieces with 0.5 teaspoon salt and 0.25 teaspoon black pepper.
Cook the fettuccine pasta in a large pot of boiling salted water according to package directions until al dente. Drain and set aside, reserving about 0.5 cup of pasta water.
While the pasta is cooking, heat 1 tablespoon of olive oil in a large skillet over medium-high heat. Add the seasoned chicken and cook until golden brown and cooked through, about 5-7 minutes. Remove chicken from skillet and set aside.
In the same skillet, melt 0.5 cup of butter over medium heat. Add the minced garlic and cook until fragrant, about 1 minute, being careful not to burn it.
Pour in 2 cups of heavy cream and bring to a simmer. Reduce heat to low and let it thicken slightly, about 3-5 minutes.
Stir in 1.5 cups of grated Parmesan cheese until melted and the sauce is smooth. If the sauce is too thick, add a little of the reserved pasta water.
Add the cooked chicken and 0.5 pound of shrimp to the Alfredo sauce. Cook for 2-3 minutes, or until the shrimp are pink and cooked through and the chicken is heated through.
Add the cooked fettuccine to the skillet with the sauce and toss to coat evenly. Season with 0.25 teaspoon black pepper and a pinch of nutmeg, if using.
Serve immediately, garnished with 0.25 cup of fresh chopped parsley.
Notes
This dish is best served immediately. For a richer sauce, you can add a splash of white wine to the garlic before adding the cream.