Grab a 2-cup liquid measuring cup. Add the garlic, chili pepper, cilantro, lime zest, ginger, sesame seeds, sesame oil, soy sauce, rice vinegar, and honey to it. Stir together until well combined.
Pour half of the mix into a bowl, add the chicken, cover, and marinate in the fridge for 30 minutes.
Cover and transfer the remaining half of the sauce that's still in the liquid measuring cup to the fridge as well.
Drain the chicken into a colander, discarding the marinade it was in.
Fry the chicken in two batches: Heat half of the vegetable oil in a non-stick pan on high heat until shimmering. Fry half of the chicken until cooked through and starting to brown on the edges. Take the chicken out of the pan and set aside.
Wipe the inside of the pan with a paper towel to remove any burned bits from it.
Repeat with the remaining chicken.
Wipe the inside of the pan with a paper towel again, then add the broccoli to it. Pour in ½ cup of cold water. Bring to a boil and boil uncovered until all the water has evaporated, stirring the broccoli around a few times.
Add the chicken back to the pan.
Add the noodles to the pan. Make sure to add the cold noodles directly out of the packet.
Whisk the corn starch into the sauce mix that's still in the liquid measuring cup. Pour into the pan.
Bring the sauce to a full boil, then take off the heat.
Sprinkle with chopped mint leaves and serve immediately.
