Preheat the oven to 350°F. Butter an 8" square pan, or eight 8-ounce ramekins., To make the cake: In a medium-sized bowl, whisk together the flour, granulated sugar, baking powder, salt, and cocoa powder. Stir in the milk, egg, vanilla, and melted butter, mixing until smooth. Stir in the nuts., Pour the batter into the prepared 8" pan. If using ramekins, place them on a parchment-lined baking sheet and portion a heaping 1/4-cup of batter into each one., To make the pudding: Mix the brown sugar with the cocoa powder, and sprinkle this mixture over the batter in the pan or ramekins. Gently drizzle the hot coffee or water over the mixture., Bake for 45 minutes for an 8" pan, or 28 to 32 minutes for ramekins, until the cake looks set and the pudding is bubbling around the edges. Remove from the oven and let cool for 15 minutes before serving. The sauce will thicken as it stands.