Make the stock: Cut the kernels from the cobs of corn and set them aside, in a bowl. Toss the cobs into a large pot with the onion, garlic, thyme, coriander, stock, and salt. Bring to a boil. Lower the heat and simmer for 45 minutes. Strain the liquid through a fine-mesh strainer, discarding the solids. There should be about 4 cups. You can store the stock in the fridge overnight.
Make the soup: Heat oil in a small pot over medium heat. Add the garlic and sweat it for 2 minutes. Add the corn kernels and sweat, stirring with a wooden spoon, for 3 minutes. Add the thyme, stock and milk, and simmer for 45 minutes.
Puree with an immersion blender, just lightly for a coarser texture. Divide the soup among six bowls. Garnish with mushrooms and bacon and a sprig of thyme.