Cover the bottom of a saute pan with 1/8 cup olive oil and heat. Add the garlic and shallot to pan, and saute until light brown in color. Add the bay scallops and rock shrimp and saute for 1 to 2 minutes. Do not overcook scallops and shrimp. Remove from heat.
In another saute pan, add the remaining 1/8 cup olive oil and heat. Add tomatoes, mushrooms, lemon juice, clam juice, white wine, and capers. Simmer for 2 to 3 minutes. Reduce liquid by 25 percent.
Add the reserved seafood to the mixture of tomatoes and mushrooms. Add the green onions. In a small bowl, make a beurre manie by combining the butter and the flour and mixing until a paste is formed. Add the beurre manie to the mixture and whisk to incorporate. Bring to a simmer and cook for 1 to 2 minutes.
Place artichoke halves in a soup bowl and ladle mixture over artichoke.
Recipe courtesy of Michael Jackson, Charlie Moss's