Heat oil in a medium saucepan over medium heat. Add garlic, ginger, jalapeño and onion; sauté about 3 minutes. Add soy sauce and brown sugar and bring to a boil. Cook, covered, over medium-low heat 8 minutes or until onion is tender. Cool mixture slightly.
Transfer to a blender; add vinegar, tomato paste, and sesame oil, and process until a chunky puree forms.
Toss shrimp with 1/4 cup of the sauce; cover and refrigerate 15 minutes.
Place shrimp in a grill basket coated with cooking spray. Grill, covered with grill lid, over medium-high heat (350° - 400°) 4 minutes or until shrimp turn pink. Serve shrimp with remaining sauce.