Grease a 9x13 inched baking dish or large casserole pan with butter or a drizzle of oil, set aside.
Add chicken thighs or chicken breasts to a medium-large pot and cover entirely with water.
Bring to a boil over medium-high heat. Once boiling, reduce heat to low and cover with a lid.
Depending on the size, boil the chicken for 15-25 minutes. Check the temperature with a meat thermometer, when inserted in the thickest part of the meat, it should read 165 degrees Fahrenheit.
Do NOT discard the water from the pot, but remove chicken from liquid and transfer to a large bowl, and shred.
In the meantime add spaghetti to the pot with water, if needed break them in half. Add a drizzle of oil, and stir. Cook per package instructions, aiming for al dente, or 1-2 minutes shy from what the package cooking time suggests, as they will be cooking in the oven as well.
In the meantime chop and dice the veggies for the recipe.
Once pasta is cooked, reserve 2 cups of cooking liquid and discard the rest. Drain the pasta.
To the large bowl with shredded chicken add cooked spaghetti, condensed cream of mushroom soup, sour cream, grated cheese, diced onion, garlic, sliced mushrooms, diced bell peppers, poultry seasoning, dried thyme, dried rosemary, and red pepper flakes. Stir to combine.
Add 1 cup of broth or reserved cooking liquid and adjust for salt and pepper. If the mixture needs more liquid, add the remaining 1 cup and stir well to combine.
Transfer the mixture to the prepared baking dish or casserole pan.
Buttery Cracker Topping:
In a medium bowl, combine cracker crumbs with melted butter, until well blended.
Spread the crumb mixture on top of the casserole.
Sprinkle the remaining 1 1/2 cup of cheese on top. Distribute evenly.
Bake for 30-40 minutes or until mixture is bubbly and cheese is fully melted.