For the shrimp: Heat the oil until it reaches 360 degrees F in wok or large skillet over medium-high heat.
Dredge the raw shrimp in the cornstarch. Fry in batches, so as not to overcrowd the pan, until their exteriors crisp up, about 4 to 5 minutes. With a slotted spoon, remove the shrimp from the oil and put them onto a paper towel-lined plate to drain.
For the sauce: In a small bowl, whisk together the brown sugar, soy sauce, vinegar, vegetable broth and cornstarch. Set the bowl aside.
Heat the canola oil in a wok or large skillet over high heat. Add the onions, garlic and ginger and stir-fry for 30 seconds. Add the bell pepper and cook for another 30 seconds. Pour in the prepared sauce and cook until the sauce thickens. Stir in the broccoli and water chestnuts and cook for 1 minute, then add the shrimp and fry for 1 minute more. Transfer the shrimp with garlic sauce to a serving bowl and serve hot with cooked rice.