1. In a 3- to 4-quart pan over high heat, combine coconut milk, rice, and 3/4 cup water. Bring to a boil, reduce heat, cover, and simmer until rice is tender to bite, about 15 minutes.
2. Meanwhile, cut peel and membrane from grapefruit. Cut between fruit and membrane to release segments into a bowl.
3. In a 10- to 12-inch frying pan, mix sugar and cornstarch. Add soy sauce, vinegar, and ginger. Stir on high heat until boiling, about 1 minute. Add shrimp and stir often until opaque but still moist-looking in center of thickest part (cut to test), 3 to 4 minutes.
4. Mound rice equally on warm plates, spoon shrimp mixture equally onto rice, and garnish with grapefruit segments, endive leaves, and basil.