Begin by bringing a large pot of salted water to a boil. Add the extra broad egg noodles and cook according to package instructions until al dente. Drain the noodles in a colander and set aside, reserving a cup of pasta water for later.
If using chicken, heat 2 tablespoons of olive oil in a skillet over medium heat. Season the pounded chicken breasts with salt and pepper, then cook for about 5-6 minutes on each side, or until cooked through and golden brown. Once done, remove from the skillet and let it rest before slicing.
In a food processor, combine the sun-dried tomatoes, fresh basil, fresh parsley, garlic cloves, shallot, pine nuts, tomato paste, and 1 1/2 teaspoons of salt. Blend until smooth, adding a splash of olive oil if necessary to help it blend. Taste and adjust seasoning as needed.
In the same skillet used for the chicken, add 1 tablespoon of olive oil. Sauté the sliced squash and chopped green bell pepper until tender, about 4-5 minutes. Add the garlic powder, onion powder, dried oregano, red pepper flakes, and pepper, stirring until fragrant.
Pour in the low sodium chicken broth, heavy cream mixed with cornstarch, milk, and fire roasted garlic diced tomatoes. Stir to combine, and bring the mixture to a simmer. Allow it to thicken slightly, about 5 minutes.
Add the cooked noodles to the skillet along with the prepared pesto. Toss everything together, adding reserved pasta water as needed to reach your desired consistency. If you opted for chicken, slice it and add it to the pasta at this stage.
Serve the Sun-dried Tomato Pesto Pasta warm, generously sprinkled with freshly grated Parmesan cheese. A drizzle of balsamic vinegar over the top adds a beautiful finish. Enjoy your delicious creation!