Place shallots, ginger, garlic, soy, lime juice, and sugar in a blender and blend until smooth. Add the green onion and oil and blend until combined. Season with black pepper, to taste. Place shrimp in a large bowl, pour the marinade over, and let marinate at room temperature for 20 minutes.

Preheat a grill to high. Remove shrimp from the marinade and grill for 1 1/2 to 2 minutes per side. Serve on brown paper bags, if desired.