Roast poblano peppers until skins char.
Peel, seed, and chop peppers.
Heat olive oil in a large pot.
Sauté onion and garlic until translucent.
Add chopped tomatoes, cook for five minutes.
Stir in cumin, chili powder, smoked paprika.
Pour in broth and bring to simmer.
Add chopped roasted poblanos.
Simmer soup for ten minutes.
Use blender for smooth texture.
Return soup to pot and stir.
Mix in heavy cream.
Add shredded cheese gradually.
Season with salt and pepper.
Simmer until cheese melts fully.
Garnish with fresh cilantro.
Serve with lime wedges on side.