Stir together all ingredients for the sauce and set aside.
Heat wok over medium-high heat, add 2 tbsp oil followed by garlic and ginger. Cook for 1 minute until very fragrant, but not browning.
Add shrimp with salt. Cook another 2-3 minutes, stirring frequently until shrimp is pink and opaque. Remove from wok and set aside.
Return wok to heat, add remaining oil followed by red onion and broccoli. Cook, stirring frequently for 3-4 minutes, until vegetable have softened and are starting to brown and char slightly.
Add sauce, and cook another 1-2 minutes until broccoli is fork tender and sauce has begun to thicken slightly--it wills till be runny. Return shrimp to pan, and toss until heated through. Serve over rice.