Start by roasting or blackening the poblano peppers in the oven, under the broiler, in the air fryer, the grill, over an open flame or in a dry skillet on the stove top. Click the link to learn how to roast poblano peppers 6 different ways!
When the peppers are blackened and blistered on all sides, cover them or place them in a resealable bag and allow them to steam for about 5-6 minutes so they can be easily peeled. Pick and rub off as much skin as possible.
On a cutting board, cut the peppers open , pull the stems, remove the seeds and discard both. Cut the peppers into small pieces and set them aside.
In a large soup pot or large Dutch oven, heat the oil and melt the butter over medium-high heat.
Add the onions, bell peppers, celery and carrots and saute stirring frequently, until the onions become translucent, about 6-7 minutes. Stir in the garlic, cumin, oregano and ground coriander and cook until fragrant, about a minute. Add the potatoes and broth making sure you have enough broth to cover the potatoes by about half an inch. If you need to, add more broth or water.
Add the bay leaves and 1 teaspoon of salt. Bring to a boil, reduce the heat, cover the pot and simmer, until the potatoes become tender, about 12-15 minutes.
Uncover the pot and discard the bay leaves. Scoop about 3 cups of chowder and transfer it to a blender. Blend until smooth. Alternatively, you can use an immersion blender and process, making sure to leave some potato chunks whole. If using a regular blender, transfer the soup back to the pot. Stir in the corn (no need to thaw it out) and chopped poblano peppers. Simmer over medium-low heat for about 5 minutes. Stir in the half and half or milk and simmer for a couple of minutes. Season to taste with salt and ground black pepper. If using chopped cilantro, you can stir it into the soup at this time. Serve with preferred toppings