Heat the olive oil in a large Dutch oven or heavy-bottomed pot over medium heat until it shimmers, then add the onion, bell pepper, carrots, celery, and ¼ teaspoon of the salt. Cook for 7 to 10 minutes, stirring now and then, until the onion looks translucent and the vegetables are tender with lightly golden edges.
Stir in the garlic, chili powder, cumin, smoked paprika, and oregano. Keep stirring for about 1 minute, until the spices smell intensely fragrant and no dry patches remain in the pot.
Add the diced tomatoes with their juices, black beans, pinto beans, vegetable broth or water, and bay leaf, then bring the mixture to a simmer. Lower the heat as needed and simmer gently for 30 minutes, stirring occasionally, until small steady bubbles rise and the beans remain whole.
Take the pot off the heat and remove the bay leaf, then blend 1 ½ cups of the chili with some of its liquid until smooth and stir it back into the pot. Use an immersion blender or potato masher instead if preferred, stopping when the chili looks thicker but still has plenty of whole beans.
Stir in the chopped cilantro, then add vinegar, red wine vinegar, or lime juice to taste and season with the remaining salt as needed. The finished chili should coat the back of a spoon and taste brighter after the acidic finish.