Step 1Slice the vanilla bean in half lengthwise and use a paring knife to scrape the seeds and pulp of one-half of the bean into a medium saucepan. Add half of the vanilla pod, the sugar and the water and bring to a boil over medium-high heat.
Step 2Meanwhile, remove the large white veins, or pith, from the tangerine segments.
Step 3Reduce the heat to low and add the tangerines to the syrup. Simmer the fruit until the tangerines look a little puffy and shiny, 3 to 5 minutes.
Step 4Strain the mixture over a bowl and discard the vanilla pod. Return the liquid to the pan and reduce over medium-high heat until it's slightly thickened and coats the back of a spoon.
Step 5Allow the syrup to cool completely and gently stir in the tangerines.
Step 1Heat the oven to 375 degrees. Brush a 10-inch round cake pan with 1 tablespoon olive oil.
Step 2Sift the flour and baking powder together and then stir in the couscous and salt. Combine 1 cup olive oil and the brandy in a small bowl.
Step 3Using a stand mixer fitted with the whisk attachment, beat the eggs, yolks and sugar on high speed for 7 minutes. Remove the bowl from the mixer and alternate folding in the dry and wet ingredients, a third at a time. Pour the batter into the prepared cake pan. Tap the pan on the counter three times to remove any air bubbles.
Step 4Bake until the cake begins to pull away from the sides of the pan and a knife inserted into the center comes out clean, about 30 minutes. The cake should be golden brown and spring back slightly when you touch the center. Cool the cake on a rack for at least 15 minutes.
Step 5Using a stand mixer fitted with the whisk attachment, whip the cream and creme fraiche together to soft peaks.
Step 6Cut slices from the cake and place them on dessert plates. Spoon some of the candied tangerines and syrup over each piece and dollop with the whipped cream.