Preheat the oven to 450 degrees . On a rimmed baking sheet, toss the corn kernels with the oil; season with salt and pepper and spread out in an even layer. Roast until browned in spots, about 15 minutes.
In a large pot, melt the butter over medium to medium-high. Add the potato, onion, jalapeno, red chile, thyme, garlic and paprika. Cook, stirring often, until the vegetables begin to soften, 3 to 4 minutes. Add the corn cobs, stock and 1 cup water. Bring to a boil and simmer until the vegetables are soft, about 10 minutes. Discard the cobs.
In a food processor, puree half the stock mixture with half the roasted corn; return to the pot. Add the remaining corn and the cream to the pot. Simmer, stirring often, until heated through, just a couple of minutes; season. Divide the soup among 4 bowls. Top with the hot sauce, scallions, parsley and radishes.