Preheat oven to 350°F. Grease and line a 4-inch pan.
Whisk flour, baking powder, and salt in a bowl.
Beat egg and sugar until pale and slightly thick, about 2 minutes.
Fold dry mix into eggs. Stir in melted butter, pistachio paste, and vanilla.
Pour batter into pan and bake 15–18 minutes or until a toothpick comes out clean.
Cool 10 minutes in pan, then transfer to a rack to finish cooling.
Whip cream and powdered sugar to soft peaks, add a touch of green gel if you want color.
Frost when cake is fully cool and sprinkle crushed pistachios on top.