Rinse the poblanos and roast them in the oven at 400F. Give them a flip after 15 minutes. They'll be mostly roasted in another 10-15 minutes, so 25-30 minutes total roasting time in the oven. Once the roasted poblanos have cooled a bit, pull off and discard as much skin as you can but don't worry about getting rid of all of it. Then de-stem and de-seed the poblanos.
As the poblanos roast you can start building the rest of the soup. Add 2 tablespoons olive oil to a saucepan over medium heat. Roughly chop an onion and add it to the saucepan along with 4 whole, peeled garlic cloves.
Once the onion is starting to brown you can add the cubed 1/2 potato, letting it cook for a couple minutes. Note that the potato is used to thicken up the soup, but you are welcome to use your preferred thickener instead.
Once the potato has cooked for a bit you can add the following ingredients: 4 cups stock, 1 tablespoon Mexican oregano, 1/4 teaspoon cumin, 1 teaspoon salt, freshly cracked black pepper, and the de-stemmed and de-seeded roasted Poblanos.
Bring this up to temp and let it simmer until the potatoes are softened -- that was about 10 minutes for this batch.
Add the mixture to a blender and combine well. Be sure to use caution when blending hot liquids -- I typically hold a paper towel over any openings to prevent a geyser.
Return the soup to the saucepan and add the corn. I used a single can of corn for this batch, drained and rinsed. Combine well and take a final taste for seasoning. I added additional pinches of Mexican oregano, cumin, and salt to this batch, but keep in mind the salt level will depend on which stock you use.
Serve immediately but don't forget to garnish! A final burst of acidity really brightens up this soup, with a squeeze of lime or a few drops of hot sauce being good options. I also added some freshly diced cilantro stems to this batch.
Store leftovers in an airtight container in the fridge.