Make stock: Cut kernels from cobs of corn and set aside, in a bowl. Toss cobs into large pot with onion, garlic, thyme, coriander, stock, and salt. Bring to boil. Lower heat and simmer for 45 minutes. Strain liquid through a fine-mesh strainer, discarding solids. There should be about 4 cups. You can store the stock in the fridge overnight.
Make soup: Heat oil in a small pot over medium heat. Add garlic and sweat it for 2 minutes. Add corn kernels and sweat, stirring with a wooden spoon, for 3 minutes. Add thyme and stock and simmer for 45 minutes. Add cream (or milk). Puree with an immersion blender, just lightly for a coarser texture. Heat gently (do not boil again of using milk). Divide soup among six bowls. Garnish with mushrooms and bacon and sprig of thyme.