Cook the green beans in a large pot of boiling water until just crisp-tender, about 3 minutes. Drain and rinse in cold water. Drain well; set aside.
Melt the butter and oil in a heavy, large skillet over medium heat. Add the shallots and garlic and saute until tender, about 2 minutes. Add the tomatoes and cook until heated through, about 3 minutes. Add the beans and cook until the juices evaporate and the beans are almost tender, stirring often, about 10 minutes. Stir in the wine and basil. Simmer 2 minutes longer. Season with salt and pepper, to taste. Transfer to a serving bowl, and serve.
Preheat oven to 400 degrees F.
Pour a heaping tablespoon of Parmesan onto a silicone or parchment lined baking sheet and lightly pat down. A silicone baking sheet is highly recommended. Repeat with the remaining cheese, spacing the spoonfuls about a 1/2-inch apart.
Bake for 3 to 5 minutes or until golden and crisp. Cool.
Yield: 8 to 10 crisps
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