Make the spice mix
Put the mint and oregano in a fine sieve set over a medium bowl. Rub the herbs against the sieve to crush them into a fine powder. In a spice grinder, grind the bay leaves, allspice, mustard seeds, cardamom seeds, and cloves to a powder and add them to the herb powder. Stir in the black pepper, cinnamon, coriander, cumin, nutmeg, and ginger. Set 1/4 cup of the baharat aside. (Save the rest for another use).
Make the chili
Put the beans in a large bowl, cover with water, and soak for 6 to 8 hours. Drain the beans, put them in a 5- to 6-quart Dutch oven or other heavy-duty pot, and add enough cold water to cover by 2 inches. Bring to a boil over high heat, lower the heat to a gentle simmer, cover partially, and cook until tender, 1 to 2 hours. Drain the beans in a colander and set aside.
While the beans cook, roast the chicken: Position a rack in the center of the oven and heat the oven to 400°F. Rinse and pat the chicken dry with paper towels. In a small bowl, combine 2 Tbs. of the baharat with 2 tsp. salt. Rub the spice mixture all over the chicken and then coat the chicken with 2 Tbs. of the oil. Put the chicken in a small roasting pan or large ovenproof skillet, and roast until an instant-read thermometer inserted into the thickest part of a thigh registers 170°F, 45 to 50 minutes. Set aside until cool enough to handle. Remove all the meat and shred into bite-size pieces. Discard the skin and bones.
Heat 2 Tbs. of the olive oil in a 5- to 6-quart pot over medium heat. Add the onion, reduce the heat to medium low, and cook, stirring occasionally, until soft, about 10 minutes. Stir in the garlic 1 minute. Stir in the bell peppers, ancho chile powder, 2 Tbs. of the baharat, and 1 Tbs. salt. Increase the heat to medium and cook until the peppers are soft, stirring occasionally, about 5 minutes. Add the tomatoes, reduce the heat to low, and simmer, stirring occasionally, until thick, about 30 minutes
Stir the chicken broth, chicken meat, and beans into the chili and continue to simmer for 20 minutes to meld the flavors. Season to taste with more salt, if necessary.
In a small bowl, whisk the yogurt, dried mint, remaining 2 tsp. olive oil, and 1/2 tsp. salt. Serve the chili topped with a dollop of the seasoned yogurt.
The baharat can be made well ahead; store it in an airtight container in a cool, dark, dry place for up to 3 months.
You can also make the chili up to 4 days before serving; store it airtight in the refrigerator and reheat gently before serving.