Spread the oil around your large wok or sauce pan. Set it to high heat and keep it there the whole time.
When it just starts smoking, add the smashed ginger slices. Don't touch for 15 seconds.
Quickly flip them and add the chicken in a single layer. Fry for 45 seconds, then flip them around and keep going for another 30 seconds.The ginger slices should be nicely browned, and the chicken no longer pink on the outside. Add shallots, white parts of scallions, and garlic. Stir-fry for 30 seconds.
Deglaze with the Shaoxing wine and stir for a few seconds.
Stir in the pre-mixed sauce, then cover with a lid. Cook for 5 minutes.
Remove the lid and turn the heat down to medium.
Stir in the green parts of scallions.
Give the corn starch slurry another good stir.
Keep simmering for a little bit to reduce the sauce. You want a little bit of liquid at the end, but the chicken shouldn't be swimming in it. Add as much of the slurry as you like (at least half); the sauce will be thicker and stickier the more you add.
Serve with rice!