Heat 1 tablespoon olive oil in a large Dutch oven or pot over medium heat. Saute the onions for 2-3 minutes until slightly translucent. Stir in the garlic, oregano, and thyme for 1 minute. Pour in white wine and reduce halfway, about 2-3 minutes.
Add the tomatoes, broth or water, and sugar, Bring to a simmer and cook, covered, for 10-15 minutes, stirring occasionally. Using an immersion blender, puree the soup until smooth. Alternatively, transfer small batches of soup to a stand blender and carefully puree, then pour back into the pot.
Add the coconut milk and parmesan cheese. Stir until the cheese melts. Mix in the fresh basil. Keep warm while you make the chickpeas.
Heat 2 tablespoons of olive oil in a large skillet over medium heat. Drain the chickpeas and pat thoroughly to dry. Add to the skillet along with the dried basil and a pinch each of salt and pepper. Spread in an even layer and cook, tossing 2-3 times for about 10-12 minutes until crisp all over.
Ladle the soup into bowls and top with a drizzle of olive oil, fresh basil and chickpeas. Serve with crusty bread.