Preheat the oven to 350 degrees F and line a 12-cup standard muffin tin with paper cupcake liners.
Put the butter, cocoa powder and chocolate in a large bowl. Pour the boiling water over and let stand 5 minutes. Whisk until smooth, and then whisk in the sugar, vanilla and eggs. Whisk in the flour, baking powder, salt and baking soda until just combined. Stir in the walnuts. Divide the batter among the prepared liners so they are about three-quarters full.
Bake until a toothpick inserted into the center comes out with moist crumbs, 22 to 24 minutes. Cool in the tins for 5 minutes, then remove and cool completely on a wire rack.
For the frosting:
Beat the cream cheese and butter on medium speed, in a large bowl, with an electric mixer until fluffy, about 2 minutes. Beat in the vanilla and lemon juice. Adjust the speed to low speed and gradually add the confectioners' sugar and beat until well combined. Frost the tops of the cupcakes and sprinkle with chopped walnuts.
When measuring flour, we spoon it into a dry measuring cup and level off the excess. (Scooping directly from the bag compacts the flour, resulting in dry baked goods.)
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