Preheat oven to 350°F (175°C). Grease and flour a 9x13 inch baking pan.
In a large bowl, cream together the butter and sugar until light and fluffy. Beat in the eggs one at a time, then stir in the vanilla extract.
In a separate bowl, whisk together the flour, baking powder, baking soda, and salt. Gradually add to the wet ingredients, alternating with the sour cream, beginning and ending with the dry ingredients. Stir in espresso powder until just combined.
Prepare the crumb topping: In a medium bowl, combine flour, granulated sugar, brown sugar and espresso powder. Cut in the cold butter until the mixture resembles coarse crumbs.
Pour batter into prepared pan and sprinkle crumb topping evenly over the batter.
Bake for 35-40 minutes, or until a wooden skewer inserted into the center comes out clean.