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Heat olive oil and butter in a large sauté pan over medium high heat.
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Add the shrimp to the pan in a single layer along with the minced garlic.
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Season with salt and pepper and cook for only a minute on each side.
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Remove the shrimp from the pan and set aside.
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Add the lime juice and white wine.
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Simmer to reduce the volume to about half before adding the shrimp back to the pan along with the red pepper, lime zest and tarragon. (You can also add another tbsp or so of butter at this stage to make the sauce a little richer if you like.)
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Toss together and cook for an additional minute or two to warm the shrimp through.
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Serve immediately tossed with your favorite cooked pasta.