Heat 1 tablespoon olive oil in a large Dutch oven over medium heat. Season shrimp with salt and pepper. Add shrimp to pot and cook 2 to 3 minutes or until pink, turning halfway through. Set aside.

Add remaining olive oil, bell pepper, onion, and garlic to pot. Cook, stirring occasionally, about 3 minutes or until tender. Stir in curry paste and ginger. Cook 1 minute, or until fragrant.

Stir in stock, coconut milk, and rice, scraping any browned bits from the bottom of the pot.

Bring to a boil over high heat; reduce heat and cook, stirring occasionally, until reduced, about 10 minutes. Stir in fish sauce and brown sugar. Remove from heat.

Using an immersion blender, puree soup in pot. Or carefully transfer soup in batches to a large food processor or blender, covering opening with a dish towel, and blend until pureed. Return soup to pot.

Stir in green onions, cilantro, basil, and lime juice. Divide soup evenly among 6 bowls and top each bowl with 3 shrimp. Serve immediately.