Preheat oven to 350°F (175°C). Line an 8×8-inch or 9×9-inch pan with foil leaving an overhang on two sides; spray the foil with nonstick cooking spray.

Make the filling: in a small bowl whisk together 2 tablespoons (25g) packed brown sugar, 1/2 teaspoon ground cinnamon, 1/4 teaspoon instant espresso powder, and 1 teaspoon all-purpose flour. Set aside.

Combine the dry cake ingredients: in a small bowl whisk 1 1/2 cups (186g) all-purpose flour, 2 teaspoons baking powder, and 1/2 teaspoon salt. Set aside.

Make the cake batter: in a large bowl stir together 1/4 cup (57g) melted unsalted butter and 3/4 cup (150g) packed brown sugar until smooth. Add 1 large egg and 1 teaspoon vanilla extract and mix until combined. Add 1/3 cup milk and 1/4 cup strongly brewed coffee or espresso (cooled), then add the dry flour mixture and stir until just combined (a few small lumps are okay).

Assemble the cake base and filling: pour about two-thirds of the batter into the prepared pan and spread into a thin, even layer. Sprinkle the reserved filling evenly over that layer. Drop spoonfuls of the remaining batter over the filling and gently spread those spoonfuls into a mostly even, thin top layer (it does not need to perfectly cover the filling).

Make the streusel: in a medium bowl whisk together 3/4 cup (150g) packed brown sugar, 3/4 cup (93g) all-purpose flour, 1 teaspoon cinnamon, and 1/2 teaspoon instant espresso powder. Add 1/4 cup (57g) melted unsalted butter (slightly cooled) and stir with a fork until the mixture forms coarse crumbs. Evenly spread the streusel over the top of the cake batter in the pan.

Bake: place the pan in the preheated oven and bake 22–28 minutes, or until the streusel is golden brown and a toothpick inserted into the center comes out clean. Begin checking at 22 minutes.

Cool and remove from pan: transfer the pan to a wire rack and cool until the cake is cool to the touch. Use the foil overhang to lift the cake from the pan, peel off the foil, and transfer the cake to a serving plate.

Make the icing and finish: in a small bowl whisk 1/2 cup (57g) powdered sugar with 1 to 2 tablespoons strongly brewed coffee or espresso (cooled) until smooth and drizzleable — start with 1 tablespoon and add up to 2 tablespoons to reach the desired consistency. Drizzle the icing over the cooled cake.

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