Heat olive oil in a large deep skillet or Dutch oven over medium-high heat.
Add the chicken pieces and cook until browned on all sides and cooked through, about 5-6 minutes. Remove chicken from the skillet and set aside.
In the same skillet, add the chopped onion and cook until softened, about 3 minutes.
Add the minced garlic and cook for 30 seconds until fragrant.
Pour in the chicken broth and whole milk, then add the broken fettuccine pasta, salt, black pepper, Italian seasoning, and crushed red pepper flakes. Stir to combine.
Bring the mixture to a boil, then reduce heat to medium-low and simmer uncovered, stirring occasionally to prevent pasta from sticking, until the pasta is tender and most of the liquid is absorbed, about 12-15 minutes.
Return the cooked chicken to the skillet and stir to combine.
Remove the skillet from heat and stir in the grated Parmesan cheese and unsalted butter until melted and the sauce is creamy.
Sprinkle the chopped fresh parsley over the top before serving.