Cut kernels from cobs and place in a large bowl. Place cobs in a medium pot and add water to cover. Bring to a boil, reduce heat to medium-low, and simmer until stock is infused with corn flavor, 40–45 minutes.
Heat butter in another medium pot over medium. Cook onion, stirring often, until translucent, about 4 minutes. Add miso and ½ cup corn stock and stir to dissolve miso. Add corn kernels and another ½ cup corn stock and cook until corn is bright yellow and just cooked through, about 2 minutes.
Let cool slightly, then transfer to a blender and blend, streaming in 2 cups corn stock to thin, until smooth. Strain soup through a fine-mesh sieve back into pot; season with salt and pepper. Heat over medium-low until warmed through.
Divide soup among bowls; top with scallions and drizzle with chili oil.