Heat oil in a large nonstick skillet or wok over medium-high heat. Add garlic, ginger and onion; cook, stirring frequently, 1 minute. Add sugar snap peas; cook until tender crisp, stirring frequently, about 3 minutes. Add shrimp; cook until shrimp are almost cooked through and turn pink; about 3 minutes.
Meanwhile, in a small bowl, mix together 1/4 cup broth and cornstarch; stir until well blended. Add remaining 3/4 cup broth and soy sauce.
Pour broth mixture into skillet, scraping up any browned bits with a spoon; stir in red pepper flakes and brown sugar. Reduce heat to low and simmer just until sauce thickens and shrimp are completely cooked, about 2 minutes. Serve over rice. Yields about 1 cup shrimp-vegetable mixture and 1/2 cup rice per serving.