Cut the kernels off the corn cobs. This is the most cumbersome part about the whole recipe, so just go ahead and knock it out first (it will be worth it!). Measure out 5 cups of kernels (save any extra kernels for another use) and reserve the cobs.
Melt the butter in a large saucepan over medium heat. Add the diced onion, and season with salt and pepper. Cook stirring occasionally, until light golden and softened, about 5 minutes. Add the jalapeño, garlic, cumin and oregano and cook, stirring, until fragrant, about 1-2 minutes longer (adjust the heat as needed, trusting your instincts). Stir in the diced potato, coating the pieces in the butter.
Pour in the water—if you’re serving the soup warm add 5 ½ cups of water, and if you’re serving it cold add 6 cups of water, as it will thicken in the fridge. Nestle in the corn cobs (it’s okay if they’re not fully submerged). Season with salt and pepper. Bring the soup to a boil, then lower the heat to a simmer, and cook for 10 minutes.
In the meantime, roast the poblano peppers either directly over a gas flame (place the peppers directly on the stove grates) or on a pan under the broiler, turning them occasionally, until they’re evenly blacked and charred. Transfer them to a bowl and cover tightly.
Remove and discard the corn cobs from the soup. Add the corn kernels, and season well with salt and pepper. Bring the soup back to a simmer; cook at a simmer until the corn kernels are bright yellow, about 1-2 minutes longer.
Working in batches, puree the soup in a blender. Stir in the lime juice and season to taste with salt and pepper—it’s really important that you season the soup well with salt (remember, we only used water!). Also, if the corn you used wasn’t very sweet, feel free to add a pinch of sugar. If you’re serving the soup warm, reheat it over low heat (feel free to add more water to thin, if desired). If serving it cold, refrigerate the soup until chilled (it will thicken as it chills).
Peel the roasted poblano peppers, discarding the black skin. Give them a quick rinse, then remove the seeds and veins. Finely chop the peppers.
Pour the soup into serving bowls and garnish with the roasted poblano peppers, Cotija cheese and a drizzle of hot sauce. If you’re serving the soup cold, you can also add diced or sliced avocado. Serve with lime wedges alongside.