Heat a large pot or Dutch oven over medium heat. Add the butter, olive oil, and onion, carrot, celery, and garlic along with ¼ teaspoon salt. Cook until the vegetables begin to soften, about 3 minutes, stirring occasionally.
If using ground turkey: Add the ground turkey and sprinkle with 1 teaspoon salt and the Italian seasoning. Break the turkey apart with a spoon and cook until browned and cooked through, about 5 minutes.
If using cooked turkey: Add the cooked turkey, sprinkle with 1 teaspoon salt, and the Italian seasoning. Cook for 1 minute to warm through.
Add the pasta, chicken broth, and milk stirring to combine.
Cover, bring to a boil, then reduce to a low simmer. Cook, covered, for 10 minutes, uncovering to stir frequently to prevent the pasta from sticking to the bottom of the pan.
Uncover and continue to simmer until the pasta is cooked and the liquid is just absorbed, an additional 2-10 minutes, stirring occasionally. Note: it's fine if the sauce looks slightly separated at this point, it should come back together with the addition of the other ingredients.
Once the pasta is just cooked, add the peas, stir, then cover and allow to sit for 5 minutes, covered, for any remaining liquid to absorb and for the peas to warm through.
Serve sprinkled with parsley and freshly ground pepper, if desired.