Ham Tetrazzini

1 lb spaghetti, broken in half
6 T salted butter, divided
2 C diced ham
8 oz white mushrooms, quartered
1/2 tsp salt, plus more to taste and for pasta water
4 cloves garlic, finely chopped
3/4 C dry white wine
3 T all-purpose flour
3 C chicken broth
8 oz pkg cream cheese, cubed
1 C frozen green peas
1 C shredded white cheddar cheese or Swiss cheese
1 C grated parmesan cheese, divided
1/2 tsp ground black pepper, plus more to taste
1/2 C panko breadcrumbs
2 T chopped fresh  parsley

Preheat the oven to 350 degrees. In a large pot of salted water, cook the pasta two minutes less than the package instructions. Reserving about 3/4 cup of pasta water, drain the pasta, rinse, and set aside. In a large pot, heat three tablespoons of butter over medium-high heat. Add the mushrooms and salt, and sauté until the mushrooms release their liquid and begin to turn golden, five to seven minutes. Stir in the garlic and cook until fragrant, about one minute. Pour in the wine and allow it to cook with the mushrooms until the liquid reduces by half, three to five minutes. Sprinkle in the flour, and cook until the flour is slightly toasted, two to three minutes. Slowly pour in the broth and stir, cooking for another few minutes until the sauce thickens. Reduce the heat to medium low. Gradually add the cream cheese, stirring until combined. Do not boil the sauce. Add the ham, peas, cheddar cheese, and 3/4 cup of parmesan. Stir to combine. Add the pepper and salt to taste.  Add the cooked spaghetti and stir to combine. Add the pasta water, about two tablespoons at a time, to loosen the sauce. (Add up to 1/2 cup of water, as needed.) Meanwhile, in a medium microwave-safe bowl, microwave the remaining two tablespoons of butter until melted. Stir in the breadcrumbs and the remaining 1/4 cup of parmesan. Spray a large (three-quart or 9 x 13-inch) baking dish with nonstick cooking spray. Pour the mixture into the pan. Drizzle the top with another ¼ cup of pasta water to keep the spaghetti from drying out. Sprinkle with the breadcrumb mixture.  Bake until the casserole is bubbly, and the crumbs are golden brown, 20 minutes. Allow to rest for five minutes before serving, sprinkled with parsley, if you like.