Heat the olive oil in a large skillet over medium-high heat until hot. Add gingerroot; cook for 1 minute.
Add shrimp, arranging in a single layer; cook for 4 minutes or until browned then flip them and move them to the side of the pan. Add garlic and white parts of the green onions to the center of the skillet; cook for 3 minutes. Stir in vinegars, water and honey; simmer for 5 minutes.
Add green parts of the green onions, the chopped cilantro and the tamari; stir to combine. Check for seasoning and to make sure it’s sweet enough for your liking.
*If you have access to an Asian market, substitute the balsamic vinegar for a more authentic black vinegar. The balsamic, although different, helps provide both tang and extra color that would be missing otherwise.
**Tamari is a dark soy sauce often found right next to traditional soy sauce.