Preheat the oven to 160 ° traditional heat. Butter 3 molds 15 cm in diameter.
In a container, sift the flours. In a large saucepan, combine the diced butter, white chocolate, powdered sugar and water. Heat over medium heat until the mixture is melted and the sugar dissolves. Pour the preparation into the bowl of the food processor and let cool. Start to mix the preparation, then add the lightly beaten eggs, the vanilla then the flour in rain while mixing. Pour the dough thus obtained into the 3 molds and bake for about 50 minutes, the inside of the cake should be moist, but cooked. Let the mussels cool on a rack then unmold and wrap in cling film.
The interior garnish: start by poaching the pears: make a syrup by heating the powdered sugar and water in a saucepan over high heat. Add the seeds of a vanilla pod. Peel the pears and cut them in half lengthwise and remove the core. Place them in the syrup and cook for 15 minutes, turn off the heat and let the pears cool in their syrup. Dice the pears (keep half a pear for decoration). Briskly whip the liquid cream and the icing sugar to obtain a firm whipped cream. Add the Philadelphia previously relaxed with a fork, whisk again. Refrigerate for final assembly.
The exterior icing: whisk the egg whites with the powdered sugar in a container over a double boiler. Stop whipping as soon as you no longer smell the sugar crystals when touching the whites. Transfer the whites directly to the food processor bowl and start whisking at high speed until the sides of the bowl cool. Gradually add the soft, soft butter while continuing to whisk, also add the pear flavor. Refrigerate for final assembly.
The topping: make a dry caramel by heating the powdered sugar in a large saucepan over medium heat. As soon as it takes an amber color, add the diced salted butter and mix vigorously. Off the heat, slowly pour in the liquid cream and mix. Pour into a container and leave at room temperature.
Assembly of the layer cake: place a small 15 cm cardboard support and place it on the serving dish. Take the first cake and fix it on the cardboard support using a knob of icing. Cover this first layer with a layer of cream cheese filling then sprinkle with diced pears. Place the second cake on top. Also apply a layer of cream cheese filling then sprinkle with diced pears. Finally, place the third cake. Spread a thin layer of frosting on top of the last cake and on the sides of the set, this layer will set the cake layers together and keep the cakes from crumbling. Chill for 30 minutes. Cover the entire layer cake with icing, smoothing everything well with a spatula. Chill for 30 minutes. Carefully pour the caramel topping on top of the layer cake. Place the small decorations and the remaining poached pear. Enjoy!
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