Start by caramelizing the white chocolate. Preheat your oven to 250 F. Spread the chopped white chocolate on a parchment-lined baking sheet. Bake for 40 to 50 minutes, stirring and spreading every 10 minutes with a spatula, until the chocolate turns a deep golden amber color and smells like caramel.
The chocolate will look clumpy and seized between stirs, but it will smooth out each time. Once deeply golden, scrape it into a bowl and stir until smooth. You will use about two-thirds for the frosting and reserve the rest for drizzling. Set aside.
Increase the oven temperature to 350 F and prepare two 8-inch round cake pans with grease and parchment paper. Whisk together the almond flour, tapioca starch, baking powder, baking soda, and salt.
Beat the softened butter and brown sugar for 4 to 5 minutes on medium-high until light and fluffy. Add the eggs one at a time, then the vanilla. Add the flour mixture in three additions alternating with the buttermilk, mixing on low speed until just combined.
Divide the batter between the two pans and bake for 26 to 30 minutes until a toothpick comes out with just a few moist crumbs. Cool in pans for 10 minutes, then turn out onto racks to cool completely.
For the frosting, beat the softened butter for 3 minutes until pale. Add about two-thirds of the caramelized white chocolate (warmed slightly so it is pourable) and beat until combined. Gradually add the powdered sugar, then the heavy cream and salt. Beat on medium-high for 2 to 3 minutes until fluffy and smooth.
Level the cake layers. Place the first layer on a cake stand and spread a generous amount of frosting on top. Add the second layer and press gently. Crumb coat the entire cake and chill for 20 minutes.
Apply the final coat of frosting, using a bench scraper to smooth the sides and create a clean finish. Warm the remaining caramelized white chocolate until just pourable and drizzle it over the top of the cake, letting some drip down the edges.
Top with white chocolate shavings and a light sprinkle of flaky sea salt. Refrigerate for 30 minutes to set, then bring to room temperature for 15 minutes before serving for the best texture.