Preheat oven to 350 degrees. Butter and flour three 8-inch pans. Bring beer and molasses to boil in a heavy medium-size non-reactive saucepan over high heat. Remove from heat and add baking soda. Let it stand about 1 hour until cool.
Whisk flour and next 6 ingredients in a large bowl until blended. Whisk eggs and both sugars in another bowl until blended. Whisk in oil, then stout mixture. Gradually whisk liquid mixture into dry mixture. Stir in fresh ginger.
Divide mixture evenly between the 3 cake pans and level tops. Bake until tester inserted into center of cakes comes out clean, about 25 minutes. Cool cakes in pans for 14 minutes, then invert onto cooling racks and allow to cool completely. (Cakes can be made 1 day ahead of serving, wrapped securely. Or wrap tightly in plastic wrap, then put into plastic zip-top bags and cool until ready to use.)
Use electric mixer to beat cream cheese, butter, and orange peel in a large bowl until fluffy. Gradually beat in powdered sugar. Chill 30 minutes before frosting cake. Decorate with candied ginger arranged in a circle at top edge of cake.
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