Begin by peeling the pumpkin, removing all seeds, and cutting it into 1-inch cubes.
Place the diced pumpkin, turmeric, salt, chopped garlic, and onions in a large saucepan. Add just enough cold water to cover the ingredients.
Set the heat to high and bring the mixture to a boil.
Once boiling, lower the heat to medium-low, cover the pot, and let it simmer for 15 minutes or until the pumpkin becomes tender when pierced.
Turn off the heat and incorporate the fresh basil or pesto into the soup.
Working in batches if necessary, carefully transfer the soup to a blender and process until you achieve a smooth consistency.
Serve hot in bowls, finishing each portion with a drizzle of organic olive oil.