Preheat the oven to 180°C (356F) and line an 8" (20cm) round springform cake tin with parchment paper.
Place pistachios in a food processor and pulse until finely ground. Set aside.
Sift and mix the dry ingredients (flour, baking powder, ground cardamom, salt) in a medium sized bowl and set aside.
Place butter and sugar in a large mixing bowl of a stand mixer fitted with the paddle attachment (you can also use a handheld electric mixer). Mix on medium speed until pale and fluffy. Use a spatula to scrape any ingredients from the sides of the bowl.
Add eggs, one at a time, and mix well after each addition (1-2 minutes). Add the milk and mix to combine.
Add the dry ingredients, alternating with ground pistachios, in two additions and mix until just combined. Do not overmix. Fold in white chocolate chips (if using) using a spatula.
Pour batter into prepared cake tin and bake for 40-50 minutes, or until a skewer inserted into the center of the cake comes out clean and cake surface is golden brown.
Let cake cool for 5 minutes in baking tin, then transfer to a wire rack to cool completely. Dust with icing sugar, slice, and serve.