Make a small slice across the stem end of each tomato; core and seed tomatoes. Sprinkle salt inside tomatoes and place them upside down on several layers of paper towels. Let stand about 30 minutes to remove excess moisture. Press dry papers into tomatoes to remove any remaining moisture.
Preheat oven to 375°F Meanwhile in a 12-inch skillet over medium heat, saute broccoli, onion and garlic in 1 tbsp of the olive oil untill onion is tender; stir often. Add shrimp, orzo and nuts, 2 tbsp of the cheese and the basil; blend well.
Spoon mixture into tomatoes. Arrange in a shallow baking dish. Sprinkle with remaining oil and cheese. Bake 20 minute or untill tops are golden.