Preheat oven to 350°F. Line an 8x8-inch or 9x9-inch pan with foil and spray with nonstick cooking spray.

Make the filling by whisking brown sugar, cinnamon, espresso powder, and flour in a small bowl. Set aside.

Make the cake by first whisking the flour, baking powder, and salt in a small bowl. Set aside.

In a large bowl, stir or mix melted butter with brown sugar until smooth. Add egg and vanilla extract, then add milk, cooled coffee, and dry ingredients. Stir until smooth (may have a few lumps).

Pour about ⅔ of the batter into the bottom of the prepared pan and spread into a thin layer. Top with filling. Drop spoonfuls of remaining cake batter on top and spread to a thin layer to mostly cover.

Make the streusel by whisking brown sugar, flour, cinnamon, and instant espresso powder in a medium size bowl. Add melted butter and stir with a fork until crumbly. Spread streusel over cake batter in pan.

Bake for 22-28 minutes, or until the crumble is golden brown and a toothpick comes out clean from the center of the cake. Cool before making icing.

Remove cooled cake from the pan using the foil overhang. Carefully remove foil and transfer to serving plate.

Whisk powdered sugar and 1 tablespoon cooled coffee, adding more coffee as needed to get icing that will drizzle. Drizzle over cake.

Slice and serve. Store in an airtight container at room temperature for several days or freeze for up to a month.