Heat the oven to 350°F. Line three 8-inch round cake pans with parchment paper and lightly coat the sides with neutral oil.
Whisk the cake flour, baking powder, and salt. Beat the dairy free butter, neutral oil, brown sugar, and granulated sugar for 3 minutes, then beat in the eggs one at a time and add the vanilla extract.
Add the flour mixture in three additions, alternating with the soy milk in two additions. Divide the batter among the pans and bake for 22 to 26 minutes, then cool the layers completely.
Combine the granulated sugar and water in a saucepan and cook without stirring until deep amber. Carefully whisk in the warm coconut cream, then simmer for 1 minute until smooth.
Remove the caramel from the heat and stir in the dairy free butter, vanilla extract, and flaky salt. Cool it completely, reserving 1/2 cup for the frosting and keeping the remainder for filling and decorating.
Beat the dairy free butter and powdered sugar until fluffy. Beat in the reserved caramel, soy milk, and fine salt until the frosting is smooth and spreadable.
Stack the cooled layers with caramel frosting and a thin drizzle of salted caramel between them. Frost the top and sides, add the remaining caramel as a drip around the top edge, and chill for 30 minutes before serving.