Heat the olive oil in a large saucepan over medium heat.
Add the chopped onions and cook, stirring occasionally, until soft, about 5 minutes.
Stir in the minced garlic, ground cumin, dried oregano, ground cloves, cayenne, and coarse salt; cook for 1 minute until fragrant.
Add the diced green chiles, drained cannellini beans, drained pinto beans, and vegetable broth; bring to a boil over medium heat.
Reduce heat to low and simmer the chili uncovered for about 60 minutes to develop flavor.
Stir in the finely chopped jalapeño (including seeds) and continue simmering.
If you want a chicken portion, scoop just under half of the chili into a separate medium saucepan, add the diced cooked chicken to that portion, and return both pots to simmer.
Simmer both the main pot and the chicken portion uncovered for another 30 minutes.
Serve the chili hot with assorted toppings: cheese, sour cream, cilantro, salsa, and lime wedges.