Preheat oven to 350°F. Line a tube pan with parchment paper on the bottom, then grease the sides with butter. Set aside.
In a large bowl, beat the butter and sugars together until light and fluffy. Add in the eggs and vanilla extract.
In a separate bowl, combine the flour, baking powder, baking soda, ground cardamom, and salt, whisking to combine. Slowly alternate folding in the flour mixture and the low fat yogurt into the wet ingredients until everything is combined.
To make the streusel, place the pistachios, cardamom, flour, and sugar in a food processor and pulse until the pistachios look well chopped. Pulse in the butter until just combined.
Pour half of the batter into the tube pan, then sprinkle with brown sugar, if using. Pour in the rest of the batter, then top with the pistachio streusel. You’ll want to squeeze the streusel into your hands, making it dense like wet sand, then sprinkle it over the batter. Bake for 50 minutes, then allow to cool slightly before removing from pan.