Position an oven rack 4 to 6 inches below the broiler and turn the broiler to high. Line a rimmed baking sheet with foil and place the 4 whole poblano peppers on it. Broil for 4 to 6 minutes, then turn the peppers with tongs and broil again.
Keep turning every 4 to 5 minutes until the skins are blistered and mostly blackened on all sides, about 12 to 18 minutes total. Do not worry if the skin looks very dark; that char is what gives the chowder its smoky flavor.
Use tongs to move the hot peppers into a large bowl. Cover the bowl tightly with a plate or plastic wrap and let the peppers steam for 15 minutes to loosen the skins.
Once cool enough to handle, rub off the blackened skin with your fingers or the back of a knife. Remove the stems and scrape out the seeds, leaving a few seeds in if you want more heat. Chop the peppers into 1/2-inch pieces; you should have about 1 cup. Skip rinsing the peppers under water, since that washes away flavor.
Dice the yellow onion and celery into small, even pieces. Mince the garlic. Peel the potatoes and cut them into 1/2-inch cubes so they cook evenly.
If using fresh corn, stand each ear upright in a large bowl and slice the kernels off with a sharp knife or corn stripper; you need 4 cups. If using frozen corn, measure it out and there is no need to thaw it.
Set your Dutch oven over medium heat and melt the butter. Add the diced onion and celery with a pinch of the kosher salt. Cook for 6 to 8 minutes, stirring often, until the vegetables are soft and the onion is translucent. Do not let them brown heavily.
Stir in the minced garlic and cook for 1 minute, until fragrant.
Add the cubed potatoes, chicken stock, bay leaves, cumin, Mexican oregano, and the remaining kosher salt. Raise the heat to high and bring the pot to a boil.
Reduce the heat to medium-low so the soup simmers gently, and partially cover the pot. Cook for 12 to 15 minutes, until the potatoes are fork-tender but not falling apart.
Remove and discard the bay leaves. Insert the immersion blender and pulse 4 to 5 times, blending only about one third of the soup. You want a creamy base with plenty of chunky potato left.
If you are using a countertop blender, ladle about 2 cups of soup into the blender, vent the lid, and blend carefully until smooth. Pour it back into the pot.
Stir the 4 cups of corn and the chopped roasted poblanos into the pot. Bring the chowder back to a gentle simmer.
Cook for 5 to 6 minutes, until the corn is tender and sweet.
Lower the heat to low so the soup stops bubbling. Pour in the heavy cream and stir until the chowder looks smooth and evenly creamy. Warm for 3 to 5 minutes, but do not let it boil, since boiling can cause cream-based soups to separate. Season with the black pepper, then taste and add more salt if needed.
Turn off the heat and squeeze in the juice of 1 lime. Adding it off the heat helps prevent the cream from curdling. Stir well and taste once more, adding a little more lime juice if you want extra brightness.
Ladle the chowder into warm bowls. Top each bowl with chopped cilantro, crumbled queso fresco, and a handful of tortilla strips. Serve with a lime wedge on the side for squeezing.