Melt 1 Tbsp. butter with oil in a Dutch oven over medium heat; add shallots, and sauté 3 to 5 minutes or until shallots are tender. Stir in garlic and tomato paste, and sauté 1 minute. Add tomatoes, sugar, and basil, and sauté 3 minutes.
Add chicken broth, salt, and pepper. Cover and bring to a boil. Reduce heat to low; uncover and simmer, stirring often, 30 minutes. Stir in 3/4 cup cream, and simmer, stirring often, 15 minutes.
Meanwhile, combine crumbled blue cheese and remaining 3 Tbsp. butter in a small microwave-safe bowl. Microwave at HIGH 25 seconds or until cheese melts. Whisk until well blended. Brush mixture evenly onto corn.
Coat a cold cooking grate with cooking spray, and place on grill over medium-high heat (350° to 400°). Arrange corn on cooking grate, and grill 12 minutes, turning every 3 minutes or until done. Let stand 5 minutes. Hold each grilled cob upright on a cutting board, and carefully cut downward, cutting kernels from cob. Discard cobs. Stir kernels into soup.
Ladle soup into bowls, and drizzle evenly with remaining cream. Garnish, if desired.