Preheat oven - Preheat oven to 350 degrees F. and spray a large casserole dish with nonstick cooking spray. Set aside.
Shred chicken - gather approximately 5 cups of cooked chicken (or turkey) and shred into small, bite-size pieces (see notes).
Boil noodles - Meanwhile, bring a large pot of salted water to a boil over high heat. Add the noodles and cook until just under al dente. Drain, rinse and set aside.
Sauté the vegetables - Heat a large, heavy-bottomed Dutch oven over medium-high heat. Add one tablespoon of olive oil and the mushrooms and cook for 3-4 minutes, stirring occasionally. Add the remaining tablespoon of olive oil and 1 tablespoon of butter to the pan. Mix in the onions with the mushrooms, stirring well to combine. Cook for 3-4 minutes, or until the mushrooms are golden and the onions are soft. Finally, add the minced garlic, salt, and pepper, mixing well to combine. Cook for an additional 1-2 minutes. Transfer to a clean plate.
Prepare the sauce - In the same heavy-bottomed Dutch oven, melt the remaining 5 tablespoons of butter over medium heat. Whisking continuously, add the all-purpose flour. Continue to whisk until roux is golden and a fully combined paste.
Add the liquid - To prevent clumping, slowly add the chicken broth. Whisk continuously. Add the lemon juice, half and half, and milk, and continue to whisk until smooth. Bring to a low simmer then reduce heat to low and sprinkle in the chopped fresh parsley.
Return the chicken - Return the chicken, mushrooms, and onions to the sauce. Gently mix in the spaghetti noodles and mix to combine. Season with additional salt and pepper, to taste.
Transfer chicken and noodle mixture to a large casserole baking dish. Sprinkle with additional fresh parsley, if desired, and top with shredded sharp cheddar cheese.
Bake - Transfer baking dish to the oven and tent with foil. Bake for 30 minutes covered, then remove the foil tent and continue to bake for an additional 15 minutes.
Serve - Allow the baking dish to rest for 5 minutes before serving. Enjoy!