Prepare a grill by adjusting the grill grate so that it’s 4 to 5 inches from the flame or heat source. Heat a gas grill to high and a charcoal grill to medium hot (the coals should be covered with light ash, and you should be able to hold your hand just over the grate for no more than 3 seconds). Put the whole tomatoes on the grate and grill, turning occasionally, until the skins crack and begin to blacken in some parts and the tomatoes soften, 7 to 9 minutes over charcoal, 12 to 15 minutes on a gas grill. Take them off the grill, core them, and coarsely chop them.
Heat the olive oil in a large soup pot over medium-high heat. Add the onion and cook, stirring occasionally, until soft, about 7 minutes. Stir in the chopped tomatoes, chicken broth, and sugar. Increase the heat, bring to a boil, turn the heat to medium, and simmer until the soup is reduced by one quarter, about 20 minutes. Let cool for 10 minutes.
In a blender, purée the soup in batches until smooth, 2 to 3 minutes per batch. Strain through a fine sieve, pressing on the solids, into a clean soup pot and bring to a simmer over medium heat. Turn off the heat and stir in the heavy cream. Taste and season with salt and pepper. To serve, ladle the soup into bowls and garnish with the chopped mint.