Preheat oven to 350°F. Blend all ingredients in bowl. Press mixture over bottom of 9-inch-diameter springform pan with 23/4-inch sides. Bake until golden, about 12 minutes. Transfer to rack; cool. Wrap outside of pan with 2 layers of foil. Reduce oven temperature to 325°F. Using electric mixer, beat cream cheese in large bowl until fluffy. Gradually beat in sugar. Scrape in seeds from vanilla bean and blend 1 minute. Beat in eggs 1 at a time. Mix in creme fraiche. Transfer filling to crust. Place cheesecake in roasting pan. Add enough hot water to roasting pan to come 1 inch up sides of springform pan. Bake cake until top is dry-looking and slightly puffed, about 1 hour. Turn off oven. Let cake cool in closed oven 1 hour. Remove from water bath. Refrigerate uncovered until cold, at least 6 hours. (Can be made 1 day ahead. Cover and keep refrigerated.) Preheat oven to 400°F. Place pineapple rings on large rimmed baking sheet. Boil remaining ingredients in small saucepan 3 minutes, stirring occasionally. Pour syrup over pineapple. Roast pineapple 12 minutes. Turn rings over; roast until tender and syrup thickens, turning rings every 5 minutes, about 20 minutes longer. Cool pineapple on sheet. Cut into 1/3-inch cubes; transfer pineapple and syrup to bowl. (Can be made 1 day ahead. Chill.) Drain pineapple, reserving syrup. Cover top of cheesecake with some pineapple; stir remainder back into syrup. Serve cake, passing remaining pineapple in syrup separately.