Make the strawberry reduction: Trim and hull 1 pound of fresh strawberries. Place them in either a food processor or upright blender and blend until you have a strawberry puree. Place the puree into a small sauce pot over medium-low heat. Cook until the contents have been reduced by half, stirring frequently to avoid burning or sticking, for approximately 20 to 25 minutes. Place your strawberry reduction in a shallow bowl. Let it cool in the refrigerator before using (at least one hour). Let it come back to room temperature before using.
Assemble all your ingredients (butter, milk, aquafaba) in advance so they are at room temperature when you use them.Preheat your oven to 350° F. Line two 6-inch round baking pans with parchment paper. Grease the sides with vegan butter or cooking spray.Prepare your strawberry powder: Add freeze-dried strawberries into your food processor. Grind until you achieve a fine powder. Place the powder through a sieve or sifter to remove any large bits. In a small cup, mix together your non-dairy milk with lemon juice and set aside (this is your vegan buttermilk). In a large mixing bowl, sift and whisk together the flour, sea salt, baking powder, baking soda, and 1/4 cup of strawberry powder.
In a large mixing bowl (or to the bowl of your stand mixer), add your sugar and lemon zest. Using your hands, massage the lemon zest into the sugar, helping to release the lemon oils. Then, add your butter. Using a hand mixer (or the whisk attachment), mix the butter into the sugar until creamy (about 2 minutes). Add your aquafaba and mix until frothy (about 30 seconds). Finally, add your strawberry reduction, vegan buttermilk, vegetable oil, strawberry extract, a little vanilla extract, and a couple drops of pink coloring and mix until fully incorporated (about 4 to 5 minutes).
Add your dry ingredients to your bowl of wet ingredients. Using the hand mixer, incorporate the dry ingredients, until all the dry ingredients have been incorporated. Do not overmix. Divide your batter equally into your prepared baking pans and bake until a toothpick inserted in the center of each cake comes out clean (around 38 to 40 minutes). Allow the cake to cool completely. (You can even wrap it in plastic wrap and place it in the fridge overnight--doing so will make frosting much easier).
Make your strawberry frosting: To a medium sauce pot over low heat, add your flour and sugar. Stir the contents with a rubber spatula so that the sugar and flour get slightly toasted (about 2 minutes). Whisk in non-dairy milk and continue to whisk over low heat until it turns into a thick paste (about 2 minutes). Pour the contents out into a shallow bowl and cover with plastic wrap so that the plastic wrap is touching the top of your roux (otherwise, it will develop an unpleasant "skin"). Place it in the refrigerator (or freezer if you want to use it as soon as possible) so that it cools down before you combine it with the butter.Once your roux has cooled, place it, together with butter and remaining strawberry powder, in a large mixing bowl or the bowl of your stand mixer. Mix together until you have a smooth, pink frosting. Make your strawberry filling: Mix your strawberries together with strawberry jam and set aside.
Assemble your cake: Once your cake has completely cooled, use a spoon or a piping bag to add enough frosting on top of the bottom layer so that it is entirely covered. Add your strawberry filling to the center, leaving some space around the margin (otherwise the strawberries will fall out when you add the second layer). Pipe or spoon more frosting over the top of the filling and spread using the back of your spoon or offset spatula. Then, gently place the second layer on top. Add frosting to the top and using your spoon or an offset spatula, smooth out the top and frost the sides.