Preheat the broiler to high. Put the quinoa in a small saucepan with 1 1/2 cups water and 3/4 teaspoon salt. Bring to a boil over high heat, then reduce heat to maintain a gentle simmer and cook, uncovered, until quinoa grains are tender, about 15 minutes. Let stand for 5 minutes. Drain off any excess water if needed, transfer to a large bowl and fluff with a fork.
Whisk 1 tablespoon oil, zest and juice from half the lime, ginger and jalapeno together in a small bowl until combined. Season with salt and pepper. Pour over the quinoa, add the scallions and cilantro and toss well.
Toss the shrimp, the remaining 1 tablespoon oil and paprika together on a baking sheet. Broil until the shrimp are opaque and cooked through, about 4 minutes. Drizzle with the juice from the remaining lime half and serve with the quinoa.
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