In the blender, puree 3 cups of the corn with the milk for 3-4 minutes, until it becomes smooth and glossy. Set aside.
Heat oil in the bottom of a medium pot and sauté onion, garlic and squash on medium heat until the onion becomes translucent, splashing in a few drops of water midway through cooking, if necessary, to prevent sticking or burning.
Turn the heat to low, and add to the pot the smooth corn puree, the remaining 1 cup of thawed corn, the thyme, parsley and salt.
Keeping the heat on low, heat the soup through and serve. Serves 4.