Bring a large pot of generously salted water to a boil. Add the fettuccine and cook according to package directions until al dente. Drain, reserving about 1/2 cup of the pasta water.
While the pasta cooks, heat 1 tablespoon of olive oil in a large skillet or Dutch oven over medium-high heat. Add the chicken, season with salt and pepper, and cook, stirring occasionally, until golden brown and cooked through, about 6 to 8 minutes. The internal temperature should reach 165°F (74°C). Transfer the chicken to a plate.
Add the remaining 1 tablespoon of olive oil to the same skillet. Add the shrimp, season with salt and pepper, and cook for 1 to 2 minutes per side, until pink and opaque. The internal temperature should reach 145°F (63°C). Do not overcook. Remove the shrimp and set aside with the chicken.
Reduce the heat to medium and add the butter to the skillet. Once melted, add the minced garlic and cook for about 30 seconds until fragrant, stirring constantly.
Slowly pour in the heavy cream, scraping up any browned bits from the bottom of the pan. Bring to a gentle simmer and cook for 2 to 3 minutes, allowing the cream to thicken slightly.
Reduce the heat to low and gradually stir in the grated Parmesan cheese until the sauce is smooth. Season with additional salt and pepper to your liking. If the sauce is too thick, thin it with a tablespoon or two of the reserved pasta water.
Add the cooked fettuccine, chicken, and shrimp back into the skillet with the sauce. Toss gently to combine everything and allow the proteins to warm through.
Serve immediately, garnished with fresh parsley if desired.