In a large deep skillet or Dutch oven, melt the butter over medium-high heat.
Add the chicken pieces to the skillet and season with salt and black pepper. Cook for 5 to 6 minutes, stirring occasionally, until the chicken is cooked through and lightly browned. Remove the chicken from the skillet and set aside.
Add the minced garlic to the same skillet and sauté for 30 seconds until fragrant, stirring constantly to avoid burning.
Pour in the chicken broth and whole milk, scraping the bottom of the skillet to loosen any browned bits.
Add the broken fettuccine pasta to the skillet. Stir to submerge the pasta in the liquid.
Bring the mixture to a boil, then reduce the heat to medium-low and simmer uncovered for 12 to 15 minutes, stirring occasionally, until the pasta is tender and most of the liquid is absorbed.
Return the cooked chicken to the skillet and stir to combine.
Remove the skillet from heat and immediately stir in the grated Parmesan cheese and crushed red pepper flakes until the sauce is creamy and smooth.
Taste and adjust seasoning with additional salt and pepper if needed.
Sprinkle chopped fresh parsley over the top before serving.