Heat 4 tbsp olive oil in an empty Dutch oven or soup pot over medium heat. Add the diced onion and a pinch of salt. Cook, stirring often, until the onions are tender and translucent, about 5 minutes.
Add the garlic, chili powder, cumin, and oregano and cook until fragrant, stirring constantly so that garlic doesn't burn, about 1 minute. Add the tomato paste and cook while continuing to stir for 1 minute.
Add the diced chili peppers, beans, vegetable broth and water to the pot. Add ½ teaspoon salt and 1/4 tsp pepper and increase heat to medium-high. Bring the mixture to a boil, then reduce heat to maintain a gentle simmer and cook for 25 minutes, stirring occasionally.
Stir in 1 tablespoon fresh-squeezed lime juice. Taste, and add more salt and/or lime juice if necessary. I usually do add a little bit more salt. For extra richness, add a little splash of olive oil and stir it in.
Divide the soup into bowls and garnish with lime wedges, cheese, tortilla strips, and other garnishes of your choice.