How to Make It
In a large saucepan, combine the tangerines with the sugar, water, cinnamon and star anise and bring to a boil. Simmer over low heat until the rind is tender and the liquid is syrupy, about 1 hour 15 minutes, stirring frequently. Scrape the compote into a bowl and let cool; discard the cinnamon stick and star anise pods.
In a food processor, finely grind the gingersnaps. Add 1 stick of the butter and process until the mixture resembles wet sand. Line the bottom of a 9-by-13-inch baking pan with parchment paper. Press the cookie crumbs evenly over the bottom of the pan and refrigerate.
In a heatproof bowl set over a pot with 1 inch of simmering water, melt the white chocolate and remaining 5 tablespoons of butter, stirring occasionally. In the bowl of a standing electric mixer fitted with a paddle, beat the cream cheese with the sugar and vanilla seeds at medium speed until smooth. Add the melted chocolate mixture and beat until combined.
In a clean bowl, using a whisk attachment, beat the cream to firm peaks. Using a rubber spatula, thoroughly mix one-quarter of the whipped cream into the cream cheese mixture, then fold in the rest. Scrape the mixture into the baking pan and spread in an even layer. Cover with plastic wrap and refrigerate overnight.
Cut the cheesecake into squares and serve with the compote.