In a Dutch oven or large stockpot, heat 1 tablespoon olive oil over medium-low heat. Add celery, bell pepper, onion, garlic, corn, chipotle and jalapeño; sauté for about 10 minutes, stirring often.
Stir in salt, pepper and stock, stirring well. Increase heat to medium and bring to a low boil. Once boiling, reduce heat and add sweet potatoes. Simmer over low for 8–10 minutes or until potatoes are tender.
Meanwhile, in a medium bowl, toss shrimp with smoked paprika, brown sugar, black pepper and ½ tablespoon olive oil. In a nonstick skillet over medium-high heat, cook shrimp 2–3 minutes per side or until cooked through. Set aside.
Pour half of the soup in a blender or food processor; purée. Combine puréed soup with the remaining soup and stir well. Gently reheat. In a small bowl, make a slurry with the cornstarch and ¼ cup of the half-and-half. Add to soup and stir well. Stir in the remaining 1¼ cups half-and-half. Stir over medium heat until the soup becomes slightly thickened. Serve immediately and garnish each serving with the cooked shrimp.