Heat the butter in a large, heavy-bottomed skillet or Dutch oven over medium heat. When the butter starts to foam, add the mushrooms. Sauté until their liquid is rendered and mostly evaporated. Add the shallots; sauté for 1 additional minute.
Sprinkle in the flour and stir continuously for 1 minute. Slowly add the broth, whisking continuously to combine with the flour and avoid forming lumps. Add in the milk, pasta, herbs, 1/2 tsp. salt, and 1/8 tsp. of pepper.
Bring the mixture to a boil, then reduce to medium-low. Cover and simmer for 15-20 minutes, stirring occasionally, until the pasta is al dente (or soft, if that's how you like it). After 10 minutes of cooking, add in the chicken or turkey, peas, pimento, and parmesan cheese. Check seasoning, adding more salt and pepper if needed.
Serve topped with parsley, if desired. (See below for optional breadcrumb topping.) Enjoy!