Preheat oven to 350 degrees F. Butter an 8-inch square baking pan.
To make fudge squares: In a large bowl, cream the butter with the sugar and egg.
In a small bowl, sift together the flour and baking powder. Add to the butter mixture. Then add the melted chocolate, being careful not to over-beat. Add the milk, vanilla, and walnuts, stirring just to blend.
Pour the batter into the prepared pan. Bake until the edges begin to pull away from the sides of the pan and the top springs back when pressed lightly, about 30 minutes. Allow the cake to cool completely. Meanwhile, make glaze.
To make glaze: In a medium bowl, combine the powdered sugar, 1 tablespoon butter, 1 oz. melted chocolate, and 1 teaspoons vanilla extract. Stir in the coffee and whisk until smooth.
Refrigerate the glaze until cool, then pour over the top of the cake and cut the cake into squares.