Start by roasting the poblano peppers. Preheat the broiler to low and broil the dry poblano in the oven for 5-6 minutes until the skin has blackened. Immediately remove the peppers from the oven and put inside a food safe airtight bag to cool or bowl covered in plastic wrap. Once the pepper is completely cooled, peel the skin from the poblano, remove the seeds and stem and dice. Return the oven to bake and preheat to 400 degrees.
Core and dice the tomatoes and dice the bell pepper. Spread the veggies on a parchment paper lined baking sheet and add the minced garlic and shallot to the pan. Drizzle with a little olive oil, 1 teaspoon of salt and fresh cracked pepper. Roast the veggies in the preheated oven for about 15 minutes until softened.
While that is cooking, boil the spaghetti according to the package instructions. Drain and set aside.
Meanwhile, into a 9x13 casserole dish, add the sour cream, 1 cup of shredded cheddar cheese and season with the smoked paprika, cumin and cayenne pepper.
Add the drained hot pasta into the sour cream cheese mixture and toss until combined.
Once the veggie mixture has finished roasting, add them to the casserole dish along with the pulled chicken and diced poblano pepper. Carefully mix everything together with the pasta and taste for any additional salt.
Once you feel the spaghetti is seasoned well, lower the temperature of the oven to 350 degrees, top the casserole with the remaining 1 cup of cheese, and bake for 25-30 minutes until everything is hot and bubbly.
Let the chicken spaghetti cool for about 10 minutes before serving and top with chopped cilantro if using.