Preheat a grill on medium high (can also use oven broiler). Cook the corn on all sides until tender and nicely charred all around. Then slice off the corn kernels.
Heat a pot over medium heat. Once hot, add the oil. Saute the onion and garlic until softened. Stir in the broth and corn. Season with salt and pepper to taste and bring to a simmer, stirring occasionally, to build flavor. Once the soup is flavorful, stir in the cream. Continue to simmer until the flavors are well blended.
Remove from the heat and allow to cool down until it is no longer steaming before placing in the refrigerator. To cool down faster place the soup into a shallow container and stir occasionally. (Can be made 1 day in advance)
Once the soup is chilled serve with cilantro and lime wedges.