Prepare chicken. Cut chicken breasts into strips and then cut those into bite-sized pieces. Sprinkle lightly with a little salt and pepper (white pepper is ideal for Chinese flavours).
Prepare broccoli. Cut broccoli into half florets and leave small ones whole. Dice the ginger and garlic and measure out the sauces (mix them in one bowl for ease).
Stir-fry broccoli. Heat a tablespoon of olive oil in a skillet over medium-high heat. Add the broccoli (cut side down) and cook for 2 minutes covered with a lid. This will help to steam the broccoli while also frying the bottom. Uncover, flip over and cook for 1-2 more minutes. Remove to a plate and set aside.
Stir-fry the chicken. Add another tablespoon of oil to the skillet and cook the chicken for 3 minutes on the first side and 3 minutes on the second side. Remove to a plate and set aside.
Add aromatics & finish the stir-fry. Add the butter, ginger and garlic to the skillet on medium-high. Cook for about 1 minute or until it's starting to turn golden and aromatic. Return the chicken and broccoli and pour in the sauces. Stir fry for about a minute together and serve.