Roast the Poblanos Roast the poblano peppers over an open flame or under the broiler until the skins are blistered and blackened. Transfer them to a plastic bag or cover with a towel and let them steam for 10 minutes. Peel, remove seeds, and slice into strips.
Sauté the Base Heat the oil in a large pot over medium heat. Add the chopped onion and cook until translucent, about 5 minutes. Stir in the minced garlic and chopped tomatoes. Cook for another 5 minutes until the tomatoes start to break down.
Simmer the Soup Add diced potatoes, tomato sauce, water, chicken bouillon, and tomato bouillon. Stir well and bring to a gentle boil. Cook until the potatoes are fork-tender, about 15–20 minutes.
Add the Final Touches Lower the heat and add the cubed queso fresco and roasted poblano strips. Pour in the heavy cream and stir gently. Cook for about 5 more minutes, just until the cheese starts to soften but doesn’t melt completely.
Season and Serve Taste and season with salt and pepper as needed. Serve hot with warm tortillas or crusty bread on the side.