Put a large, deep skillet or wok over medium-high heat. Add half the oil, swirl it around, and immediately add half the garlic and ginger. Cook for 15 seconds, stirring, then add the scallion, cabbage, carrots and mushrooms. Raise the heat to high and cook, stirring occasionally, until the mushrooms soften and the cabbage and carrots scorch a little in places and become soft, 5 to 8 minutes, then transfer everything to a plate.2. Turn the heat down to medium, add the remaining oil, let it get hot, and add the remaining garlic and ginger. Stir, then add the chicken. Raise the heat to high, stir the chicken once, then let it sit for 1 minute before stirring again. Cook, stirring occasionally, until the chicken has lost its pink color, 3 to 5 minutes. Don't worry about the chicken cooking through; it will. And don't worry about the chicken bits that stick to the bottom; you'll get them later.3. Turn the heat down to medium, return the vegetables to the pan, and toss once or twice. Add the sugar if you're using it, along with the soy sauce, and toss again. Sprinkle with salt and pepper and add the liquid. Raise the heat to high and cook, stirring and scraping the bottom of the pan, until the liquid is reduced and you've scraped up all the bits of chicken. Garnish with chopped scallions and serve with the lettuce leaves for wrapping.