Preheat the oven to 350℉.
Make the cake first. In a large mixing bowl, sift the matcha, flour, baking powder, and baking soda. Stir in the salt. Set aside.
Now, in another large mixing bowl, or the bowl of a stand mixer, add the vegan butter, and beat with a hand mixer or the paddle attachment for the stand mixer, until the butter is smooth.
Add the sugar and beat together until completely combined. Scraping down the sides of the bowl as needed.
Add the applesauce, and vanilla, and continue to mix until fully incorporated.
Now, while the mixer runs, add the dry ingredients a little at a time to the wet ingredients, alternating with the non-dairy milk, until everything is fully incorporated and the batter is smooth.
Pour the batter into a 13x9-inch pan that has been lined with parchment paper. Smooth it out evenly.
Bake for 35-45 minutes or until a toothpick comes out clean from the center of the cake.
Once the cake is done, let it cool for a few minutes while you make the matcha syrup. Whisk together the matcha powder and water, making sure the powder has dissolved.
In a large measuring cup or a large cup with a spout so you can easily pour from it, whisk the non-dairy milk, sweetened condensed coconut milk, and vanilla until fully combined. Pour the matcha into the mixture and whisk again.
Poke holes all over the cake with a fork, a straw, or, I like to use a chopstick. Then pour the matcha syrup all over the top of the cake.
Put the cake in the fridge and let it cool completely.
Once the cake has cooled, make the frosting. Add the vegan butter, vegetable shortening, and vegan cream cheese to a large mixing bowl or the bowl of a stand mixer.
Using the whisk attachment for a hand mixer or the stand mixer, whip together until smooth.
Add the powdered sugar, a little at a time, until the frosting is smooth.
Add the crushed strawberries and a pinch of salt. Whip together.
Scoop the frosting onto the top of the cake and smooth it out.
Top with strawberries if desired, then serve.