In a large mixing bowl, whisk together the whole-wheat pastry flour, milk, water, olive oil, eggs, sugar, and salt until smooth. Let the batter rest for at least 30 minutes to allow the flour to hydrate, which will result in tender crêpes.
Heat a non-stick skillet or crêpe pan over medium heat. Lightly grease the pan with a bit of olive oil. Pour about 1/4 cup of batter into the center of the pan, swirling to spread it evenly. Cook for about 2 minutes until the edges begin to lift, then flip and cook for another minute. Transfer the crêpe to a cooling rack and repeat with the remaining batter, stacking the cooked crêpes as you go.
In a stand mixer or a large bowl using a hand mixer, beat the softened butter and cream cheese together until fluffy. Add in the vanilla extract and mix well. Gradually add the sifted powdered sugar until fully incorporated, scraping down the sides of the bowl as needed.
Once the crêpes are completely cooled, place one crêpe on a serving plate. Spread a thin layer of cream cheese frosting over the crêpe, then sprinkle with chopped pistachios and coconut flakes. Repeat the layering process with the remaining crêpes, frosting, and toppings, finishing with a crêpe on top.
Place the assembled cake in the refrigerator for at least one hour to set. This will help the layers meld together and make serving easier. Once chilled, slice and enjoy your Pistachio Crêpe Cake!