Heat the oil in a large skillet over medium heat. Add the onion and carrots and cook, stirring occasionally, until soft, 6 to 8 minutes.
Add the garlic and curry and cook, stirring, until fragrant, 2 minutes.
Add the rice, 2 1/2 cups water, 1/2 teaspoon salt, and 1/2 teaspoon pepper and bring to a boil. Reduce heat to medium-low, cover, and simmer for 15 minutes.
Season the shrimp with 1/2 teaspoon salt and 1/4 teaspoon pepper and nestle them in the partially cooked rice. Cover and cook until the shrimp are opaque throughout, 4 to 5 minutes. Fold in the basil and serve.