1. Bring rice, 3 cups water, and 1/4 teaspoon salt to a boil in a 3- to 4-quart heavy saucepan, then reduce heat to low and simmer, covered with a tight-fitting lid, 45 minutes (rice will be cooked but still wet).
2. Stir in maple syrup, coconut milk, pecans and vanilla extract and bring to a boil over high heat, then reduce heat to low and simmer, uncovered, stirring occasionally, until mixture is thick and rice is tender but still slightly chewy, about 30 minutes.
Stir pudding and divide among 8 bowls. drizzle remaining coconut milk over pudding. Rice pudding keeps, covered and chilled, 5 days.