Season the chicken strips with salt and pepper.
Cook the noodles until soft but not soggy, about 4 minutes. Drain, plunge in iced water and drain again.
Use the upper half of the cabbage leaves only; reserve the lower half for other use. Slice the leaves crosswise, about an inch wide.
Heat the cooking oil until it starts to smoke. Stir fry the chicken until lightly browned, about 8 minutes.
Add the garlic and sliced onion. Stir fry for about a minute then add the carrot slices. Stir fry for another minute. Add the cabbage and onion leaves, sprinkle with salt and pepper, and cook for two more minutes.
Pour in the oyster sauce and the sugar. Stir well. Taste and add more salt and pepper if necessary. Remember that you will be adding the noodles which will require seasoning too so make allowances.
Add the noodles, toss and stir to coat the noodles with the sauce and oil. Turn off the heat, drizzle with sesame seed oil and toss a few more times.
Serve the chicken lo mein immediately.