Melt 2 tablespoons of the butter in a medium saucepan over medium heat. Add half the garlic, and cook, stirring, until soft, about 2 minutes. Add the quinoa, 2 1/3 cups water, 1/4 teaspoon salt and a few grinds of pepper, and bring to a simmer, stirring. Cover, reduce the heat to medium-low and cook until the quinoa is tender (the little white tails become visible) and the liquid is the consistency of a thin porridge, 10 to 15 minutes. Remove the saucepan from the heat, and whisk in the Parmesan and half the parsley. Cover and keep warm.
Meanwhile, season the shrimp with 1/4 teaspoon salt and a few grinds of pepper. Heat the oil in a large nonstick skillet over medium-high heat. Add the shrimp in a single layer (it's OK if they touch), and cook until the underside turns pink, about 2 minutes. Turn the shrimp, add the remaining garlic and cook until the shrimp begin to curl and turn totally pink, about 2 minutes more. Add the wine, 2 tablespoons water and the remaining parsley, reserving a pinch for garnish. Once the liquid has reduced by half, swirl in the remaining 2 tablespoons butter until smooth. Divide the quinoa and shrimp among 4 bowls, top with the pan sauce and sprinkle with the reserved parsley.
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