Mix 1 tablespoon olive oil, 1 garlic clove, dried parsley, black pepper, and red pepper flakes together in a small bowl; mix well. Add shrimp, turn to coat, and refrigerate for 30 minutes.
Cut off the ends of the zucchini and use a spiralizer on the thinnest setting to create the zoodles.
Heat remaining olive oil and butter in a large skillet over medium-low heat. Saute shallot for 3 minutes; add remaining garlic and cook for an additional 30 seconds. Add shrimp and cook until bright pink on the outside and meat is opaque, about 2 minutes per side. Add lemon juice, wine, lemon zest, and salt. Cook and stir for 1 minute.
Remove the skillet from heat and add zucchini; stir for 2 to 3 minutes. The residual heat will cook the zucchini.
Divide onto 2 plates, top with fresh parsley, and serve.
The two medium zucchini together should weigh about 1 pound.
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