Place the freeze-dried strawberries in a blender and process until they become mostly powder. A few small pieces is okay, but any larger pieces may end up a bit chewy in the frosting.
In a stand-mixer fitted with a paddle or whisk attachment (or large bowl using a beaters) beat the vegan cream cheese and vegan butter for 1 minute on high speed until smooth. Add the confectioner's sugar a cup at a time, strawberry powder, and the vanilla and beat on medium-speed until combined and creamy. Add 1 tbsp at a time of plant-based milk if the frosting is too thick. Depending on the brand and consistency of vegan cream cheese and vegan butter, you may or may not need to add any milk. Vegan cream cheese frosting is similar to true dairy cream cheese frosting in that it does not get quite as fluffy as vegan buttercream.
If the cakes are domed on top, slice a thin layer off the tops with a long serrated knife so that they are flat. As this is a very moist cake, it shouldn't have much dome.
Place a small dollop of frosting on the serving plate to prevent the cake from sliding around. Place one cake layer on the plate and evenly cover with frosting. Try using an ice cream scoop, using 2-3 scoops of frosting in between each layer. This helps ensure even amounts of frosting between each layer which is apparent once the cake is cut. Repeat for the second layer. Use the same number of scoops for the top layer but work it down the sides of the cake as well - the frosting will be very thin - you're creating a crumb coat. This traps the cake crumbs so that they don't get caught in the final frosting layer which can appear a bit messy. Chill the cake in the fridge for about an hour, then apply the final frosting to the top and sides of the cake, smoothing out with an offset spatula or cake scraper. You may not need all of the frosting. Top with fresh strawberries. Cover leftover cake with plastic wrap and store in the fridge.