In a large pot, heat the olive oil over medium heat. Add the diced onion and sauté until translucent, about 5 minutes.
Stir in the minced garlic, bell pepper, and jalapeño peppers. Cook for another 3-4 minutes until the peppers are softened.
Add the diced tomatoes (with their juice), vegetable broth, cumin, chili powder, smoked paprika, salt, and pepper. Bring the mixture to a boil, then reduce the heat and let it simmer for 15 minutes.
Stir in the chopped roasted poblano peppers and simmer for an additional 10 minutes.
Remove the pot from heat and stir in the shredded Monterey Jack cheese until melted and creamy.
Serve hot, garnished with a dollop of sour cream, fresh cilantro, and a squeeze of lime juice.