Preheat the oven to 350 degrees Fahrenheit. Spray an 8-inch round cake pan with cooking spray and cover the bottom with parchment paper. Set aside.
Next, make the cake. In a food processor, pulse together the pistachios and ½ cup of the sugar until very fine. Set aside.
In the bowl of a stand mixer, combine 1 cup of sugar, almond milk, butter, eggs, Greek yogurt and vanilla using the paddle attachment until a thick paste forms.
In a separate bowl, whisk together the flour, baking soda and salt.
Add dry ingredients to wet ingredients and mix until well combined. Fold in pistachio mix.
Bake in 350-degree oven for 50 minutes, or until a cake tester inserted into the center comes out clean. Set on a rack to cool for about 20 minutes, then turn out of pan onto rack to cool completely. You may need to use a butter knife or inserted spatula around the edges of the cake to loosen it from the pan.
While cake is cooling, make the buttercream. In a clean stand mixer fitted with a clean paddle attachment, combine all of the frosting ingredients. Mix until ingredients form the buttercream frosting texture.
Either frost the cake once it has cooled completely, or wrap the cake in plastic wrap and place the buttercream in a resealable container in the refrigerator until ready to serve. Be sure to bring the buttercream back to room temperature before attempting to frost the cake. Cake can be kept out at room temperature for up to two days, but for best preservation, keep it refrigerated, which will make it last up to one week.