Preheat the oven to 350°F (175°C). Light a fire under your patience and grease a 9-inch cake pan.
Pulse the pistachios in a processor until fine. Don’t turn them into dust—tiny crunch is good. Set aside a couple of tablespoons for garnish.
In a bowl, whisk flour, baking powder, and salt. In another bowl, cream butter and sugar until pale and fluffy.
Add eggs one at a time, beating well after each. Mix in vanilla and pistachio paste (or ground pistachios) until incorporated.
Alternate adding dry ingredients and milk to the batter, starting and ending with dry ingredients. Beat until just combined—overmixing is for bread, not cake.
Pour batter into the prepared pan. Smooth the top with a spatula. Bake 28–35 minutes, or until a toothpick comes out clean.
Let the cake cool in the pan for 10 minutes, then turn out onto a rack. If you’re fancy, drizzle with glaze and sprinkle with the reserved pistachios.