In a resealable plastic bag, toss the shrimp with the garlic and onion powders, paprika, oregano, fennel seeds, dried thyme, 1 tablespoon of the oil and 1/2 teaspoon each of salt and pepper until coated. Let stand at room temperature for 30 minutes.
Meanwhile, preheat the oven to 425°. In a food processor, pulse the basil, parsley, rosemary, thyme leaves, garlic and cheese. Add 2 tablespoons of the oil; puree until smooth. Season with salt and pepper.
In a saucepan, combine the quinoa, water and the remaining 1 tablespoon of oil. Season lightly with salt and bring to a boil. Cover and simmer over low heat until the quinoa is tender, about 15 minutes. Let stand for 5 minutes. Transfer to a bowl; keep warm.
On a baking sheet, roast the shrimp for about 8 minutes, until curled and pink. Cut the shrimp into thirds and add to the quinoa with the pistou. Toss well, season with salt and pepper and serve.