Preheat the oven broiler on high.
Place the poblano peppers on a baking sheet and broil for about 10 minutes, turning occasionally, until the skins are charred and blistered.
Transfer the peppers to a bowl and cover with plastic wrap. Let them steam for 10 minutes.
Peel the skins off the peppers, remove the seeds and stems, and chop the peppers into bite-sized pieces.
Heat olive oil in a skillet over medium heat. Add diced onion and cook for 3-4 minutes until softened.
Add minced garlic and cook for 1 minute until fragrant.
Add ground beef to the skillet and cook until browned, breaking it up with a spoon. Drain excess fat.
Transfer the cooked beef, onions, and garlic to the slow cooker.
Add chopped poblano peppers, diced tomatoes with green chilies, fire-roasted diced tomatoes, pinto beans, black beans, beef broth, ground cumin, smoked paprika, chili powder, dried oregano, cayenne pepper, salt, and black pepper to the slow cooker.
Stir all ingredients to combine.
Cover and cook on low for 6 hours.
About 10 minutes before serving, stir in the shredded Monterey Jack cheese until melted.
Ladle the soup into bowls and garnish with chopped fresh cilantro.