Heat olive oil in a large pot over medium heat. Add the onion and cook for 5 to 7 minutes, stirring occasionally, until softened and translucent.
Add the garlic, chili powder, cumin, oregano, and paprika. Stir and cook for 1 minute.
Add the adobo sauce and stir to combine.
Pour in the chicken broth, then stir in the beans and shredded chicken. Bring the mixture to a boil, then reduce heat to low and simmer for 10 minutes.
In a small bowl, whisk together cornstarch and cold water to form a slurry. Slowly pour the slurry into the pot while stirring to thicken the chili. Continue to simmer for 5 minutes, stirring occasionally, until the chili has thickened slightly.
Reduce the heat to low or turn off completely. Stir in the sour cream and shredded Monterey Jack cheese and stir until melted and fully incorporated.
Ladle into bowls and serve hot, garnished with more cheese, jalapeño, lime, and cilantro.