In a small bowl, whisk together paprika, turmeric salt and pepper. Set aside.
Heat a soup pot to medium-low and add olive oil. When oil is lightly shimmering, add onion. Cook, stirring frequently, until onion is softened and translucent, around 6-8 minutes. Turn heat to low and add garlic and spices. Cook, stirring, another minute, until garlic is softened and fragrant. You can add a splash of water or two to prevent sticking/burning.
Add remaining ingredients, stir to incorporate and bring soup to a simmer (for me, this usually means turning the heat back to medium-low). Simmer for 30 minutes, or until butternut squash is fork-tender and the soup has thickened in consistency. Carefully use tongs or a spoon to pull basil leaves out. Discard.
Use an immersion blender to puree the soup, or carefully blend in a blender or food processor—this usually requires 2 batches.
Serve immediately with a sprinkle of fresh shredded basil and any other garnish of choice.