Preheat the oven to 400 degrees F. Bring a pot of salted water to a boil.

Heat the olive oil in a 12-inch oven safe skillet (like cast iron or ceramic) over medium heat. Add the shallots and onion with a pinch of salt. Cook for 5 minutes, until slightly softened. Stir in the squash. Add another pinch of salt and pepper. Stir in the smoked paprika, cumin and red pepper flakes. Cook the squash, stirring often, until it gets caramelized and browned and slightly tender, about 8 to 10 minutes.

At this point you can boil the pasta. Shave 2 to 3 minutes off the cook time - you want it slightly firm since we are baking it. If the pasta is done before you need it, spray or drizzle with olive oil so it doesn't stick together.

Add the stock to the skillet and bring the mixture to a simmer. Simmer for a few minutes until the squash is tender enough to mash. Mash half of the squash in the skillet with a wooden spoon or a fork. Taste the squash and season with more salt and pepper if necessary.

Add the pasta to the squash skillet. Stir in the reserved pasta water and stir until everything is combined and incorporated. Stir in the parmesan chicken, the cooked chicken and the spinach, 1 handful at a time.

Top the pasta with the grated cheese and the pickled jalapeños. Bake for 15 to 20 minutes, until golden and bubbly and cheese. Remove and sprinkle with extra parmesan. Serve immediately!