Place chicken in a large pot. Fill with water (about 4 quarts). Bring to a boil. Let boil 20 minutes or until chicken is cooked through. Remove chicken and shred with two forks (or with the paddle attachment of a stand mixer). Reserve cooking liquid (broth) in pot.
Melt 2 tablespoons butter in a large skillet. Add mushrooms, 1/4 cup white wine, 1 tsp salt, and 1/2 tsp pepper. Cook over medium heat for 8 to 10 minutes, stirring occasionally, or until liquid has evaporated. Remove mushrooms from skillet. Set aside.
Bring reserved broth to a boil. Break spaghetti in half and add to boiling liquid. Cook 8 min or until noodles have reached desired doneness. Drain, reserving broth.
Add 6 tablespoons butter to same skillet used for cooking mushrooms. Sprinkle flour over butter, whisking to combine. Cook 2 minutes. Slowly add 2 cups reserved broth, whisking constantly. Slowly add milk, remaining 1/4 cup wine, remaining 1 tsp salt and 1/2 tsp pepper. Bring to a boil. Reduce heat and let cook until thickened. Remove from heat; stir in 1 cup parmesan cheese.
Add mushrooms, chicken, chopped olives, pimientos, and peas to sauce. Stir to combine. Taste and add more salt and pepper if needed. Add cooked spaghetti and stir.
Add to a 9 x 13 baking dish. Bake at 350 degrees 10 minutes or until golden brown and bubbly. Top with remaining parmesan before serving.