Stir all of the ingredients together in a large bowl. Butter a 9-inch springform pan. Press the crumb mixture onto the bottom and about halfway up the sides of the pan.
To make the filling:
Beat the cream and goat cheeses in the bowl of an electric stand mixer with the paddle attachment until light and fluffy. Add the creme fraiche and beat to combine. Add the eggs, 1 at a time, beating after each egg is added, until thoroughly combined. Beat in the sugar and vanilla until just combined.
Pour the filling into the prepared crust. Put on a baking sheet in the preheated oven and bake for 55 to 60 minutes. Rotate the baking sheet halfway through the cooking process. If the cheesecake starts to color, tent the springform pan with aluminum foil.
Remove the cheesecake from the oven and let it cool completely before serving, as it continues to set as it cools. It is best to refrigerate overnight before serving. Cut the cake into wedges and serve with Vanilla Pineapple Compote.
Vanilla Pineapple Compote:
Combine the brown sugar, water, rum, and vanilla beans in a saucepan over medium heat. Squeeze the lemon juice into the pan and stir to combine. Bring to a simmer, add the pineapple and stir until well mixed. Simmer until the liquid has reduced to a syrupy consistency and the pineapple is soft.
Let cool and serve as an accoutrement to yummy desserts like goat cheese cheesecake!