Move the oven rack to the lower-middle position. Preheat the oven to 325 degrees F.
Generously butter a 10-inch bundt pan.
Dust the pan with flour and tap out the excess flour.
MAKE CAKE BATTER:
In a medium bowl, whisk together cake flour, baking powder, salt, and ground cardamom. Set aside.
In the bowl of a stand mixer fitted with a paddle attachment, beat butter and sugar on medium-high speed until creamy and lightened in color and fluffy, about 1-2 minutes.
Add eggs, lemon zest, and salt and beat until just combined.
Add the flour and buttermilk to the mix, alternating between the dry ingredients and buttermilk in three parts, starting and ending with the flour mixture.
Fold in the pistachios.
BAKE CAKE:
Pour the cake batter into the prepared cake pan. Smooth the batter into an even layer.
Bake in the preheated oven for 70-80 minutes, rotating the pan halfway through baking or until a toothpick inserted comes out clean.
COOL CAKE:
Move the cake to a wire rack to cool for 15 minutes.
Then, invert the cake onto the rack and cool completely for about 45-60 minutes.
MAKE LEMON FROSTING:
Add all of the ingredients into the bowl of a stand mixer.
Pulse the mixer until the powdered sugar is mixed in. Then, increase the speed to medium and beat for 2 minutes, or until light and creamy.
TO FINISH:
Once the cake is cooled, spread the frosting evenly over just the top of the cake.
Garnish with pistachios.
Slice and serve.
Notes
If you don't like lemon flavor or lemon zest, just leave it out. You will still have a delicious pistachio cake!