Heat the olive oil in a large heavy-bottomed pot over medium-high heat.
Add the onions, and sauté, stirring frequently. When they are just translucent, add the garlic and celery. Sauté for 3-5 minutes until the celery has softened.
Add the cumin, smoked paprika, oregano, and salt, and add the potatoes. Stir to combine.
Add the shorn corn cobs (not the kernels!) and pour the vegetable broth over the top.
Bring the broth to a boil, then reduce the heat, cover the pot, and simmer until the potatoes are tender - approximately 10-15 minutes.
Remove the corn cobs from the pot, and add the corn kernels and red pepper in. Stir, and cover the pot to simmer for 10 minutes more.
Remove from the heat and purée half of the soup if desired.
Add the coconut milk, and stir to combine.
Serve garnished with corn kernels and cilantro, if desired.