Place the poblanos on a baking tray and bake for 30 minutes, flipping halfway.
Add 1 tablespoon of the oil to a large frying pan and bring the heat to medium high.
Add 4 ears of corn and cook for 15 minutes rotating frequently until all sides are charred. Repeat this process with the remaining 4 ears of corn. Set aside
Add the remaining 2 tablespoons of oil to a large pot and bring the heat to medium high.
Add the onion and garlic and sauté for 8 minutes.
Add the potatoes, chile powder, cumin, Mexican oregano, salt, pepper, smoked paprika, and broth. Bring to a boil and then reduce heat to low and cook for about 15 minutes or until the potatoes are tender.
When the poblanos are done, remove from the oven and move to a cutting board. Peel the skin and remove seeds and stems. Chop the peppers.
Cut the corn off of the cobs and add it and the chopped poblano peppers to the soup.
Blend half of the soup, off heat, with an immersion blender.
Add the cream and return pot to the stove. Heat on low for 5 minutes.