Preheat the oven to 350°F. Line an 8×8-inch square pan with parchment paper, leaving overhang on the sides. *Note, if you did double the batter, preheat the oven to 325F instead.
In a medium bowl, mix the flour, baking powder, baking soda, salt, and espresso powder. Set aside. In a large bowl, using a hand mixer, or in a stand mixer fitted with the paddle attachment, cream the butter and sugar on medium-high speed. Once light and fluffy, scrape down the sides of the bowl and add the egg and egg yolk, followed by the vanilla extract. Add the sour cream and mix until combined. Add the dry ingredients and mix to form a thick batter.
Scoop the batter into the prepared pan. Smooth the top with an offset spatula, then top with the crumbs, using your hands to break the crumb dough into pieces of various sizes. Some larger pieces should be about the size of a walnut, and smaller pieces can be pea-sized. Variation is good—just make sure to scatter them evenly.
Bake for 30–32 minutes, until a toothpick or paring knife inserted into the center of the cake comes out clean. Remove from the oven, let cool, and top with powdered sugar.
