Heat wok or large skillet over high heat. Add 2 tbsp peanut, canola, or other oil with a high smoke point. Add 1 tbsp garlic and 1 tbsp ginger. Brown the chicken in small batches, adding oil, garlic and ginger each time. Leave enough garlic and ginger to add in last step. Remove chicken and cover to keep warm.
Add mushrooms to wok. If there is not sufficient oil to coat the mushrooms after the chicken is done, add a little more. Cook the mushrooms until soft. If you add a tablespoon or so of water, the mushrooms will cook more quickly.
Stir in broccoli and cover to steam. Again, add about 1 tbsp of water if it looks dry. Steam 2-3 minutes or until bright green, stirring occasionally.
Stir in colored peppers and the chopped stalk of the bok choy. Again, add about 1 tbsp of water if it looks dry. Cover and steam 2-3 minutes, stirring occasionally.
Add cooked chicken, chopped bok choy leaves, remaining ginger and garlic, oyster sauce and 1 tbsp of water if needed to thin the oyster sauce. Do not cover. Stir occasionally until bok choy leaves are slightly wilted.
Serve plain, as we often do, or over rice or Asian noodles, as desired.