Begin by preheating your oven to 350 degrees and greasing an 8x8 square pan. In a large bowl, combine the first nine ingredients: 1 cup flour, 3/4 cup sugar, 2 tablespoons unsweetened baking cocoa, 2 teaspoons baking powder, 1/4 teaspoon salt, 1/2 cup milk, 2 tablespoons vegetable oil, and 1/2 cup chopped walnuts.
Mix these ingredients until just combined, then pour the batter into the prepared pan, spreading it evenly across the bottom.
In a separate small bowl, whisk together 3/4 cup packed brown sugar and 1/4 cup unsweetened baking cocoa until thoroughly blended. Add 1 1/2 cups of boiling water to this mixture and stir until the brown sugar dissolves completely.
This step is fundamental to creating the pudding sauce layer, so make sure the water is truly boiling for ideal results. Slowly pour the water mixture directly onto the cake batter already in the pan. Pour deliberately and steadily to avoid creating a large hole in the center of the batter—the water will sink beneath the batter and create the signature pudding layer as it bakes.
Place the pan in the preheated 350-degree oven and bake for 40 minutes, or until a toothpick inserted into the cake layer comes out with just a few crumbs clinging to it. The toothpick should not come out completely clean, as some moisture from the pudding layer below is expected.
Allow the cake to cool for a few minutes before serving warm, scooping portions directly from the pan to capture both the tender cake and the rich chocolate pudding sauce beneath.
