Preheat the oven to 350°F (175°C). Grease and flour an 8-inch round cake pan.
In a medium bowl, whisk together the all-purpose flour, baking powder, baking soda, salt, and finely chopped pistachios. Set aside.
In a large bowl, beat the eggs and granulated sugar together until pale and slightly thickened, about 3 minutes.
Add the Greek yogurt, vegetable oil, vanilla extract, lemon zest, and honey to the egg mixture. Mix until well combined.
Gradually add the dry ingredients to the wet ingredients, folding gently with a spatula until just combined. Do not overmix.
Pour the batter into the prepared cake pan and smooth the top with a spatula.
Bake for 35 to 40 minutes, or until a toothpick inserted into the center of the cake comes out clean.
Remove the cake from the oven and allow it to cool in the pan for 10 minutes.
Turn the cake out onto a wire rack and let it cool completely before serving.