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Boil water in steamer or large saucepan over high heat. Reduce heat to medium-high. Place green beans in steamer basket; cook for 1 to 2 minutes, or until tender-crisp and bright green. Place in ice water bath to stop cooking process. Set aside.
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To make dressing, combine 3 Tbsp. oil and vinegar in a small bowl; whisk to blend. Season with salt and pepper if desired. Set aside.
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Heat remaining 1 tsp. oil in large nonstick skillet over medium-high heat.
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Add shallots; cook, stirring frequently, for 5 to 6 minutes, or until shallots are slightly caramelized.
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Add peaches and oregano; cook, stirring frequently, for 5 to 7 minutes, or until peaches are soft.
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Combine peach mixture, green beans, and dressing in a large bowl; toss gently to blend.
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Divide evenly between eight serving plates; serve immediately.