Preheat the oven to 350 degrees F. Spray and line with parchment a 9-by-9-inch baking pan; spray the parchment as well.
For the crumb topping: In a medium bowl, mix the flour, brown sugar, cinnamon, instant coffee powder and salt. Add the melted butter and mix until crumbs form that you can clump together in your hand. Set aside.
For the cake: In a medium bowl, whisk together the flour, baking powder, baking soda, cinnamon, salt and cardamom. In a smaller bowl, whisk together the coffee and sour cream until smooth.
In the bowl of an electric mixer fitted with the paddle attachment, beat the butter and sugar together until light and fluffy. Add the eggs, one at a time, mixing until each is well combined. Then add the vanilla extract and beat until the mixture is light and fluffy.
Starting and ending with the dry ingredients, alternate adding the flour mixture and the coffee mixture to the stand mixer; mix each addition well, scraping the bowl each additions.
Pour the batter into the prepared baking pan and top with crumb topping, spreading it evenly. Bake for 45 minutes or until a toothpick comes out clean.
Remove the cake from the oven and allow to cool for 20 to 30 minutes before cutting and serving.