For the soup, heat the olive oil in a 3 to 4 quart pot over medium heat. Add the carrots and onions, and cook, stirring frequently, until the vegetables are soft, 5 to 7 minutes.
Add the dried basil, salt and pepper and stir for about 1 minute. Mix the tomatoes and their juice with the vegetable broth. Stir, bring to a boil, then reduce heat and simmer gently, uncovered, for 20 to 25 minutes. Add the minced fresh basil and cream and cook for about 5 minutes more.
Puree the soup with a stick blender or blender. Taste and adjust seasonings.
Meanwhile, for the crostini, preheat oven to 375 degrees F (190 degrees C). Line a baking sheet with parchment paper. Place baguette pieces on prepared pan.
Combine butter, granulated garlic, salt, and minced parsley in a bowl. Use a spatula to mash and stir until well mixed. Add shredded Parmesan and stir until a paste forms.
Spread about 1 tablespoon garlic-Parmesan paste on each baguette slice.
Bake in the preheated oven until lightly browned and crisp, 12 to 15 minutes, or until lightly browned and crisp.
To serve, ladle the soup into serving bowls and serve with crostini. Garnish with fresh basil.
