Heat the butter over medium in a pan with rounded edges (or a saucier, if you have one). Test the butter by adding a tiny pinch of flour; when the butter bubbles like it’s lightly frying the flour, whisk in all the flour.

Keep stirring while cooking the mixture—after the first 5 minutes, it will begin to change color and smell nutty. It will continue to darken, so keep stirring as it cooks.

Once the roux turns light golden brown and begins to smell like popcorn, add half the broth and stir until the roux is completely thinned. Remove from the heat and set aside.

Heat the oven to 400° and oil a flat sheet pan with 2 tablespoons of the olive oil. Toss the squash cubes on the pan to coat with the oil and season with salt and pepper.

Roast for 25 minutes, turning the pan and stirring the squash once, midway through.

Meanwhile, heat the remaining tablespoon of olive oil in a soup pot over medium-high heat. Mix the chili powder, cumin, salt, black pepper, cayenne pepper and oregano in a bowl. Dredge the cubed chicken in this spice mixture.

Add the chicken to the olive oil and cook for 5 minutes, or until no longer pink. Remove the chicken to a plate, and add the onion to the pot—cooking until caramelized (about 5 minutes), then remove to the plate.

Add the garlic and cook for about 30 seconds. Add the chicken, onions and any remaining spice mixture from the bowl to the pot. Add the bell pepper, Hatch chiles, tomato paste, beans, tomatoes and the remaining broth, then stir in the roux.

Cook for 10 minutes over low/medium-low heat, so that the chili bubbles softly—stirring occasionally. Finally, add in the squash, cooking until it’s warmed throughout.

Stir in the fresh lime juice and garnish each bowl as desired.