In a small bowl, combine brown sugar, flour, and cinnamon. Cut in butter until the mixture resembles coarse crumbs. Set aside.

In a mixing bowl, whisk together flour, baking powder, baking soda, cardamom, cinnamon, and salt. In another bowl, beat butter and granulated sugar until creamy. Add eggs, one at a time, beating well after each addition. Mix in sour cream and vanilla extract.

Gradually add the dry ingredients to the wet ingredients, mixing just until combined.

Spread half of the batter into the prepared 9-inch cake pan. Sprinkle half of the crumble topping over the batter. Add the remaining batter and smooth the top. Sprinkle with the remaining crumble topping.

Bake in a preheated oven at 350°F (175°C) for 40-45 minutes, or until a toothpick inserted into the center comes out clean.

Let the cake cool in the pan for 10 minutes, then transfer to a wire rack to cool completely. Slice and serve.