Heat the olive oil in a large saucepan over medium heat.
Add the chopped onions and cook, stirring occasionally, until softened, about 5 minutes.
Stir in the minced garlic, ground cumin, dried oregano, ground cloves, cayenne pepper, and coarse salt and cook for 1 minute until fragrant.
Add the diced green chiles, drained cannellini and pinto beans, and vegetable broth. Bring to a boil over medium heat.
Reduce heat to low to maintain a gentle simmer and cook uncovered for about 60 minutes.
Stir in the finely chopped jalapeño pepper; include seeds if you want more heat.
If adding chicken to half the batch, scoop just under half of the chili into a separate medium saucepan and stir in the diced cooked chicken.
Simmer both the main (vegetarian) pot and the chicken portion, uncovered, for an additional 30 minutes.
Serve the chili hot with assorted toppings such as cheese, sour cream, cilantro, salsa, and lime wedges.