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Bake garlic naan:
Preheat oven to 400°F. Toss together naan, 2 tablespoons butter, 1/2 tablespoon garlic, and 1/4 teaspoon salt on a rimmed baking sheet; spread into an even layer. Bake until golden brown, about 12 minutes. Let cool completely on baking sheet, about 15 minutes.
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Cook onions and spices:
Meanwhile, heat 2 tablespoons butter in a large saucepan over medium. Add onion; cook, stirring often, until softened and starting to caramelize, about 8 minutes. Add curry powder, smoked paprika, and remaining 2 tablespoons garlic; cook, stirring often, until lightly browned, about 2 minutes.
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Simmer soup base:
Add 1 1/2 cups water to saucepan; cook, stirring constantly and scraping up any browned bits, for 1 minute. Stir in tomatoes, sugar, and remaining 1 teaspoon salt. Bring to a boil. Reduce heat to medium; simmer, stirring occasionally, until tomatoes break down and soup thickens, about 25 minutes. Stir in vinegar.
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Blend and serve:
Process soup using an immersion blender (or in an upright blender) until smooth. Serve topped with naan. Drizzle with remaining 1 tablespoon butter.
Make Ahead and Storage
Store in the refrigerator in an airtight container for up to 4 to 5 days. Crispy naan can stay for one week at room temperature. Or freeze soup in an airtight container for up to three months. Thaw in the refrigerator overnight before reheating.