Boil salted water in a large pot. Add fettuccine and cook until al dente. Drain and set aside.
In a large skillet over medium-high heat, heat 1 tablespoon of olive oil. Add the chicken pieces, season with salt and pepper, and cook for 7-10 minutes until cooked through and no longer pink. Remove the chicken from the skillet and set aside.
In the same skillet, add 1 tablespoon of olive oil. Add shrimp, season with salt and pepper, and cook for 2-3 minutes per side until pink and opaque. Remove shrimp and set aside.
In the same skillet over medium heat, melt the butter. Add the minced garlic and cook for 1 minute until fragrant. Pour in the heavy whipping cream and bring to a gentle simmer, stirring occasionally.
Slowly add the grated Parmesan cheese until combined and smooth. Add salt and pepper to taste.
Combine the cooked pasta, chicken, and shrimp with the sauce, tossing gently to mix and warm them.
Divide the pasta over plates and garnished with parsley if desired.