Heat the olive oil in a large pot or Dutch oven over medium-high heat. Add the onion and bell pepper and cook for 4 to 5 minutes, stirring now and then, until the onion softens and the edges take on a little color.
Stir in the garlic and cook for 30 seconds, just until fragrant. Do not let it brown.
Add the ground turkey. Break it up with a wooden spoon and cook for 6 to 7 minutes, letting it sit undisturbed for 1 to 2 minutes at a time so it browns instead of steaming. Season with salt and pepper as it cooks.
Push the turkey to the sides, add the tomato paste to the center of the pot, and cook it for 1 minute, stirring it into the hot oil until it turns a darker red and smells rich, almost sweet. Stir in the chili powder, cumin, smoked paprika, oregano, and cocoa and cook for 30 seconds more.
Pour in the chicken broth and scrape up every browned bit from the bottom of the pot. That is pure flavor, do not leave it behind.
Add the black beans, kidney beans, fire roasted tomatoes with their juices, and the tomato sauce. Stir everything together well.
Bring the chili to a boil, then reduce the heat to low, cover, and simmer for 20 minutes, stirring a couple of times so the beans do not settle and stick.
Uncover and simmer 5 to 10 minutes more if you like it thicker. Taste and adjust the salt. For a little brightness, a squeeze of lime over each bowl at the table works wonders.
Serve hot with your favorite toppings: shredded cheese, a dollop of Greek yogurt or sour cream, sliced green onions, diced avocado, or crushed tortilla chips.