Add 1 tablespoon of oil to a large skillet over a medium-high setting. When the oil is hot, add the chicken, sprinkling with salt and pepper to taste.
Cook the chicken for about 10 minutes, until browned on the outside, and thoroughly cooked on the inside. Remove from the heat and set aside for now.
Add the other 1 tablespoon of olive oil to a saucepan. When the oil is hot, add the minced ginger and garlic and saute for about 3 minutes, until fragrant and slightly browned. Do not burn.
In a bowl, add the honey, lemon zest and juice, cider vinegar, soy sauce, and cornstarch. Whisk until thoroughly combined.
Pour the lemon honey mixture over the garlic and ginger in the saucepan, and stir together. Turn the heat up to high, and bring to a boil for about 2 minutes. The sauce should thicken and will probably become slightly darker.
Add the cooked chicken chunks to the skillet, and stir to coat on all sides, keeping the setting on high.
Stir the chicken and cook for about 3 to 4 minutes as the sauce caramelizes and sticks to the chicken.
Remove from the skillet and garnish with green onions and sesame seeds.