Preheat the oven to 325°F and grease a loaf pan
Add the pistachios to a food processor and mix on high speed until very fine. If you don't have a food processor, you can place the pistachios in a zip top bag and crushed with a rolling pin. The final result should have the same texture as almond flour.
Add your room temperature butter to a large bowl, and beat with a hand mixer or stand mixer fitted with a paddle attachment until light and fluffy
Add the salt, sugar, flour, ground pistachios, and baking powder to the mixing bowl. Mix on low speed until well combined. The texture will look similar to shortbread cookie dough.
Add the vanilla extract and one egg. Mix on low speed until just combined. Add the remaining eggs one at a time, mixing after each egg is added. Be sure not to over mix. The final batter should be thick and smooth.
Pour the batter into the greased baking tin and smooth out the top. Place in the middle rack of the oven and bake for 60 - 75 minutes until a toothpick comes out clean. A few moist crumbs are okay - raw batter is not.
Remove from the oven and let cool in the tin for 5 minutes. Then turn out onto a wire cooling rack. The pound cake can be served warm or at room temperature.