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 powder and cook, stirring, until fragrant, 2 minutes.
Add the rice, 2½ cups water, and ½ teaspoon each salt and pepper and bring to a boil. Reduce heat and simmer, covered, for 15 minutes.
Season the shrimp with ½ teaspoon salt and ¼ teaspoon pepper. Nestle them in the partially cooked rice. Cover and cook until the shrimp are opaque throughout, 4 to 5 minutes. Fold in the basil.