Heat the olive oil in a large Dutch oven over medium-high heat until it shimmers. Add the turkey, press it into an even layer, and leave it alone for 3–4 minutes until the underside is deep golden brown. Break it up and cook until no pink remains, about 3 minutes more.

Add the onion and bell pepper with a pinch of salt. Cook, scraping up the browned bits, until the onion is translucent and smells sweet, about 5 minutes. Stir in the garlic and cook just until fragrant, about 30 seconds.

Push everything to the sides, add the tomato paste, chili powder, cumin, smoked paprika and oregano to the center, and stir for 60 seconds. The paste should darken to brick red and the spices should smell toasty, not burnt.

Add the squash, tomatoes with their juices, beans, broth, salt and pepper. Bring to a boil, then lower the heat to a gentle simmer with small, lazy bubbles.

Simmer uncovered, stirring every 10 minutes, for 25–30 minutes. The chili is ready when a squash cube crushes easily against the side of the pot and a spoon dragged across the bottom leaves a trail that slowly fills back in.

Turn off the heat and stir in the lime juice. Taste and adjust salt. Rest 5 minutes, then serve with your favorite toppings.