Line a baking sheet with aluminum foil and place poblano peppers on top. Set your oven rack directly underneath the broiler and turn the broiler on high.
Broil poblanos in the oven for 5 minutes, or until the skin is blackened and blistered. Carefully flip them over and broil for another 5 minutes, or until the skin is blackened and blistered on all sides.
Remove them from the oven, loosely cover the baking sheet with aluminum foil or plastic wrap to keep in some of the heat to help them steam, and let them sit for 5 minutes.
Pull and rub off as much of the loose skin on the peppers as possible. It doesn't have to be perfect. (View some step-by-step photos on how to roast poblano peppers.)
Transfer poblanos to a cutting board, slice open, and discard the stems and seeds. Dice into small chunks and set aside.
Melt butter in a large pot or Dutch oven over medium-high heat. Add the onions, celery, and carrot. Cook for 8 minutes, stirring occasionally, until the carrot has begun to soften.
Add garlic and cook for one minute.
Add potatoes, 4 cups of broth, salt, bay leaves, salt, cumin, coriander, Mexican oregano, and black pepper. Raise heat to high and bring to a boil. Reduce heat to medium-low, cover, and simmer for 10 minutes until the potatoes are tender and cooked through.
Discard the bay leaves, then carefully scoop out 4 cups of chowder from the pot and transfer to a blender. Cover and pulse a few times until mostly smooth.
Pour the blended chowder back into the pot and stir in the corn and chopped poblanos to the pot. Bring to a simmer.
Add heavy cream and shredded cheese. Stir until the cheese has completely melted.
Bring pot back to a simmer and cook for 5 more minutes.
Serve and garnish with chopped cilantro and a squeeze of fresh lime juice in each bowl
Be careful when blending hot liquids! Try not to overfill your blender and hold the blender lid down with a kitchen towel to prevent splashing and spilling.
If you don’t have frozen corn, you can use canned corn as well. Just make sure to drain and rinse it first under water.
This chowder can vary in spice level. Poblanos peppers are typically mild but sometimes you get a spicy batch! If you’re concerned that it might be too spicy, be sure to remove all the seeds and veins from the peppers after roasting them.
For spicier chowder, leave the seeds and veins intact when preparing the peppers.