Preheat the oven to 350℉. Line a 9×9 baking tin with parchment paper and set aside.

Brown all the butter: 
In a light-bottomed saucepan over medium heat, melt 1 cup of butter (from the Cake and Crumble sections), stirring occasionally with a heatproof spatula. As the butter melts, it will begin to bubble gently and then more wildly. Keep stirring and scraping along the bottom to prevent burning. Within a few minutes, the bubbles will grow smaller, the foam will turn golden, and you’ll notice a rich, nutty aroma. As soon as you start to see brown specks at the bottom, remove from heat immediately. It can burn fast from here. Divide the butter exactly in half. Set aside.

Make the crumble topping: In a bowl, mix the brown sugar, white sugar, flour, cinnamon, cardamom, and salt. Stir in half of the browned butter until the mixture resembles damp sand and forms clumps. Refrigerate to firm it slightly.

Combine the wet ingredients: – In a large bowl, whisk together the remaining browned butter, brown sugar, orange zest, and cardamom. Then incorporate the Greek yogurt, eggs, vanilla extract, and orange juice and whisk until mostly smooth.

Mix in the dry ingredients: In a separate bowl, whisk the flour, baking powder, baking soda, and kosher salt until well combined. Fold the dry ingredients into the wet ingredients and stir just until combined. Avoid overmixing for a soft, tender crumb.

Assemble the cake: Pour half the batter into a prepared baking pan. It will be a little thick, so you will need to use your spatula to spread the batter down. Remove the crumble from the fridge and sprinkle about half (or a little less than half) of the crumble over the first layer of cake. Then, spoon the remaining batter over the first layer of crumble. Again, the batter will be thick so harder to spread. Don't worry about being perfect. Sprinkle the remaining crumble, making sure some clumps are larger than others.

Bake the cake: Bake at 350°F until golden and a toothpick comes out clean, and the center is no longer wiggly, about 40–50 minutes. Cool completely before icing and slicing to allow the crumb to set.

Make the icing – Whisk the icing sugar, orange juice, a pinch of orange zest, and vanilla bean paste (or extract) until smooth. Don't use too much orange zest as it can make the icing bitter – just use enough to get the visual speckles of orange zest. Drizzle over the cooled cake.