Begin by roasting the poblano peppers over an open flame or in a preheated oven at 450°F (230°C) for about 15-20 minutes, turning occasionally until the skins are charred. Transfer to a bowl and cover with plastic wrap to steam for 10 minutes. Peel off the skins, remove the seeds, and dice the peppers.
In a large pot, heat the olive oil over medium heat. Add the diced onion and sauté for about 5 minutes until soft and translucent.
Stir in the minced garlic and cook for an additional 1-2 minutes until fragrant.
Add the diced potatoes and corn kernels along with the roasted poblano peppers. Stir to combine.
Pour in the vegetable broth and bring to a boil. Reduce heat and let simmer uncovered for 15-20 minutes until the potatoes are tender.
Use an immersion blender to puree the chowder until smooth, or blend portions in a blender for desired consistency.
Return the chowder to low heat and stir in the heavy cream and smoked paprika. Season with salt and pepper, and heat through for another 5 minutes.