Cut the corn kernels off the cobs and set aside. Use the back of a chef's knife to scrape the juice from the cobs into a medium saucepan. Add the cobs to the saucepan along with the sprig of thyme and enough water to just cover the cobs. Bring to a boil, then reduce the heat to a simmer and cook for 30 minutes. Remove the cobs and thyme and then strain the corn broth into a medium bowl or large measuring cup. (You should have about 4 cups. Add water if you have less. If you have more than 4 cups, then return to the saucepan and simmer until reduced to that amount.)
Heat the oil in the saucepan over medium heat. Add the onion, garlic, thyme leaves and a pinch each of salt and pepper. Cook, stirring occasionally until the onion is soft, 3 to 5 minutes. Add the reserved corn kernels and cook until the corn is just cooked through, 2 to 4 minutes. Stir in the corn broth and remove from the heat.
Working in batches, puree the corn mixture in a blender until very smooth, 3 to 4 minutes per batch. Return all the soup to the saucepan and simmer until hot, about 5 minutes. Season with salt and pepper.
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