PREP: Remove the husks and silk from each cob of corn. Cut the corn kernels off all the cobs except for one corn cob. Keep the bare cobs; we'll be using them! Thinly slice the shallots.
SAUTÉ SHALLOTS: Grab a large pot (big enough to hold the bare corn cobs). Place over medium heat and add coconut oil. Once oil is melted, add in the shallots and cook, stirring frequently until they've softened and have started to slightly caramelize, about 10 minutes. (Don't rush this, we're adding in loads of flavor). Add garlic and sauté for 30 seconds.
SIMMER SOUP: Add in corn that you cut off the cobs and salt & pepper to taste (I add 1-1/4 tsp salt and 1/2 tsp pepper). Add the bare corn cobs and the entire corn cob you set aside earlier. Cover the cobs with 6 cups of chicken stock. Bring soup to a rolling boil and then reduce the heat to medium-low and simmer (uncovered) for 10 minutes. At this point, remove the whole ear of corn and set it aside to cool.
BLEND SOUP: Cook the soup for 10 more minutes, then remove the bare cobs, and discard. Remove soup and let cool for a bit (if it's too hot, it will explode out of the blender!). Add the soup (in batches -- don't overfill the blender or it will explode) to a powerful blender (Note 3). Blend until very smooth-- this takes a few minutes to get it super smooth (and even longer in a less powerful blender). (If you can't get it totally smooth to your liking, you can pass the soup through a strainer back into the pot.)
FINISH SOUP: Meanwhile, cut the corn from the reserved corn cob. Return the soup back to the pot along with the cut corn and fresh basil. Stir through and taste. Adjust by adding more salt/pepper to taste. (If needed, you can add a dash of sugar to emphasize the corn sweetness or a pinch of red pepper flakes if you'd like some kick). If soup is too thick or too thin, see Note 4. Serve soup in bowls and garnish with additional basil if desired.