Butter ten 2/3-cup soufflé dishes (or ramekins); dust with sugar; arrange on a baking sheet.
Combine milk and 1 cup coconut in medium saucepan; bring to boil; remove from heat and cover; let stand 30 minutes; strain; discard coconut (or make up some rice pudding and stir it in); return milk to saucepan and boil until reduced to 2 cups, about 15 minutes (can be made 1 day ahead; cover and chill).
Preheat oven to 425°F.
Whisk yolks, 1 cup sugar and flour in large saucepan until blended; gradually whisk in milk and rum; bring to boil over medium heat, whisking constantly; pour into large bowl; stir in vanilla; cool custard until warm, stirring occasionally, about 8 minutes.
Beat whites in large bowl to soft peaks; gradually add ¼ cup sugar; beat until stiff but not dry; fold 1/3 of whites into warm custard; fold in remaining whites; fill soufflé dishes halfway with batter; sprinkle 1 ½ tsps coconut over each; spoon remaining batter over, dividing equally; top each with about ½ tsp coconut.
Place baking sheet with soufflés in oven and bake soufflés until puffed and golden, about 15 minutes; sift confectioners’ sugar over them; serve immediately, passing warm chocolate sauce separately; Remember – A SOUFFLE WAITS FOR NO ONE!
For Chocolate-Rum Sauce: Stir chocolate and cream in medium saucepan over low heat until melted and smooth; mix in rum.