Combine broth, Neufchatel, and 1 tsp. cornstarch in a small saucepan. Bring to a simmer, whisking constantly over medium heat. Set aside.
Tear bread into large pieces and place in a food processor with a steel blade attachment. Process to fine crumbs. Transfer the crumbs to a large bowl. Add mushrooms to the food processor and pulse to chop finely. Add the mushrooms to the bowl. Add turkey, 1/4-cup Parmesan, garlic, Italian seasoning blend, pepper and gently knead to combine. Form into 16 meatballs, about 2 scant tablespoons each.
Coat the bottom of a 6-qt. slow cooker insert with cooking spray. Arrange meatballs in the bottom of the insert. Pour the sauce over the meatballs. Cover and set the slow cooker to low for 4 hours.
When the timer on the slow cooker has 30 minutes remaining, bring a large pot of water to a boil. Cook spaghetti according to package instructions. Drain well. Divide pasta between 4 bowls. Top with four meatballs each and spoon sauce over the meatballs and pasta. Sprinkle the remaining 2 Tbs. Parmesan over the top and garnish with parsley, if using.