Using a large pot or Dutch Oven, over medium heat, heat the olive oil until hot and fluid. Once the oil is hot, add the chopped onion, red bell pepper, carrots, celery and 1/2 tsp salt. Cook on medium heat for about 8 minutes stirring occasionally until the onion becomes translucent and the vegetables are tender.
Once the vegetables are tender, add the garlic, chili powder, cumin, smoked paprika, oregano, and cayenne pepper. Continue stirring constantly to mix the spices evenly for about one minute.
Next, add in the mild chiles, diced tomatoes with their juices, drained pinto beans, drained black beans, vegetable broth and bay leaves. Stir well to evenly combine all flavors and then let the chili heat to a gentle simmer. Continue cooking the chili for an additional 30 minutes while adjusting the heat as necessary to keep a gentle simmer. Stir the chili regularly to keep the flavors mixing. Once the chili has been simmering for 30 minutes, remove from the heat and remove the bay leaves.
To achieve the a smoother texture for the chili, blend briefly with an immersion blender while in the pot. This will make the chili slightly more smooth and unleash more flavors.
Lastly, add in the chopped cilantro, lime juice and remaining 1/2 tsp salt and stir to combine evenly.
Serve chili hot in individual bowls and topped with your favorite toppings like shredded cheddar cheese, sour cream, sliced avocado, or tortilla chips.