Combine the crêpe ingredients: add 2 cups whole-wheat pastry flour, 2 cups 2% milk, 1 cup water, 4 teaspoons olive oil, 4 eggs, 2 tablespoons sugar, and 1/2 teaspoon salt to a blender. Blend until the batter is completely smooth and well combined. Transfer the batter to a covered container and refrigerate at least 1 hour.

Heat a crêpe pan or a wide nonstick skillet over medium heat and lightly spray or oil the surface.

Stir or gently shake the chilled batter, then measure a scant 1/4 cup of batter for each crêpe. Pour the batter into the center of the hot pan and immediately tilt and rotate the pan at about a 45° angle in a circular motion so the batter forms a thin, even layer with no holes.

Cook the crêpe until the edges begin to turn golden and lift away from the pan, about 1 minute. Use a thin spatula to loosen an edge, then flip the crêpe with the spatula (or carefully with your fingers) and cook the second side about 30 seconds.

Transfer the cooked crêpe to a plate and stack finished crêpes. Repeat steps 3–4 until all batter is used. When finished, place the stacked crêpes in the refrigerator to cool for at least 1 hour before assembling.

While the crêpes cool, make the filling: in a large bowl, beat 3/4 cup softened butter and 12 ounces cream cheese together with an electric hand mixer until light and fluffy. Add 3 teaspoons vanilla extract and mix until combined.

With the mixer on low, gradually add 3 cups sifted powdered sugar. Once incorporated, increase the speed to high and beat until the frosting is light and fluffy, about 5 minutes. Place the frosting in the refrigerator until ready to assemble.

Assemble the cake on a serving plate: place one cooled crêpe on the plate, drop a heaping 2 tablespoons of the cream cheese frosting onto the center, and use an offset spatula to spread a thin, even layer over the entire crêpe.

Sprinkle a heaping 1/2 tablespoon of the finely chopped pistachios over the frosting, then place another crêpe on top and gently press to adhere. Repeat this layering (frosting, pistachios, crêpe) until you reach the final crêpe.

For the top layer, spread the remaining frosting over the top and along the sides in a thick, smooth layer.

Press the 3/4 cup coconut flakes evenly into the top and sides of the cake, then refrigerate the assembled crêpe cake for at least 2 hours to set before serving.