To Make the Cake
1. Position a rack in the center of the oven and heat the oven to 350 degrees F. Coat the bottoms and sides of three 9-by-2-inch round cake pans with nonstick baking spray or butter and line with parchment circles.
Sift together the four, baking powder, and salt into a medium bowl.
2. In the bowl of a stand mixer fitted with the paddle attachment (or in a large bowl, using a handheld mixer), cream the butter, corn syrup, and sugar on medium speed until light and fluffy, about 4 minutes.
3. Whisk together the eggs, crème fraiche, and vanilla in a small bowl, then pour the mixture into the creamed butter and beat until smooth. Scrape the bottom of the sides of the bowl and the paddle and mix for 30 seconds. With the mixer on low speed, add the dry ingredients in two batches, mixing for 30 seconds after each addition. Scrape the bowl again and mix for 15 seconds.
4. Divide the batter among the prepared cake pans, spreading it evenly. Bake for 15 minutes. Rotate the cakes and bake for an additional 10 to 12 minutes, until the cakes appear firm and have a matte finish and a toothpick inserted in the center comes out clean. Let the cakes cool completely in the pans on cooling racks. Wrap the cakes in plastic wrap and refrigerate until you are ready to assemble the cake.
To Make the Frosting:
1. In the bowl of the stand mixer fitted with the paddle attachment (or in a large bowl, using a handheld mixer) beat the butter on a medium speed until very soft and creamy, about 3 minutes. Scrape the sides and bottom for 1 minute. Pour in the corn syrup and vanilla and mix until thoroughly incorporated.
2. Scrape the sides and bottom of the bowl and beat on low speed as you stream in the melted white chocolate. Add the salt and continue beating until the buttercream is shiny and fluffy, about 3 minutes. Scrape the bowl once more and beat for 30 seconds on medium-high speed. (The buttercream can be covered and stored in the refrigerator for up to 2 weeks.)
To Assemble the Cake:
1. Place one cake layer top side up on a cake stand or turntable. Slide four strips of parchment under the edges of the cake to catch and stray frosting. Using an offset spatula, spread the frosting evenly over the top of the layer. Top with 1 ½ cups of the raspberries.
2. Repeat with another cake layer with more frosting and layer of raspberries. Stack the third layer on top and press down gently to even the layers. Using an offset spatula, frost the sides and top of the cake with remaining frosting.
3. Take a handful of coconut at a time and press onto the sides of the cake until the sides are covered. Sprinkle the remaining coconut on top of the cake. Chill for at least 30 minutes before serving.