Assemble ingredients.
In a large soup over high heat, bring enough water to cover the tomatoes to a boil. Once the water is boiling, submerge the whole tomatoes in the water just until the skins split, approximately 30 seconds to 1 minute. Using a slotted spoon or spider, remove the tomatoes to a colander and set them aside in your sink.
Empty the pot of water and lower the heat to medium-high. Add the olive oil and the onions. Cook for 8 minutes, stirring a few times. Reduce the heat to medium-low and stir in the garlic, basil, and oregano. Continue to cook until the onions have softened and the garlic and herbs are fragrant.
While the aromatics are cooking, remove the skins from the tomatoes and chop them into chunks.
Turn the heat up to medium-high. Add the tomatoes to the onions and garlic and stir to combine. Bring to a rolling simmer. Turn the heat down so that the soup is just simmering. Cover and cook the tomatoes for 8 minutes.
Stir in the sun-dried tomatoes, broth, coconut milk, salt, and pepper. Allow the soup to come back to a simmer. Continue to cook until the sun-dried tomatoes have softened, approximately 5 more minutes.
Remove the pot from the heat and blend until smooth with an immersion blender. Alternatively, blend in batches in a countertop blender. Return the soup to the heat to warm it up before serving.
Adjust the seasoning if necessary. Ladle into bowls and serve with fresh basil leaves and crostini.