In a 2-cup liquid measuring cup or small bowl, combine the garlic, sliced Fresno chili, chopped cilantro, lime zest, grated ginger, sesame seeds, toasted sesame oil, soy sauce, rice vinegar, and honey; stir until well blended.
Pour half of the sauce into a bowl, add the chicken pieces, cover, and refrigerate to marinate for 30 minutes; set the remaining half of the sauce in the measuring cup in the fridge to use later as the stir-fry sauce.
After marinating, drain the chicken in a colander and discard the marinade from the chicken's bowl.
Heat half of the vegetable oil in a non-stick pan or wok over high heat until shimmering. Fry half the chicken in a single layer until cooked through and lightly browned on the edges, about 2–4 minutes per side depending on piece size. Transfer to a plate and wipe the pan clean with paper towels.
Add the remaining oil, then fry the second half of the chicken the same way; transfer to the plate when done.
Wipe the pan again, add the broccoli florets and 1/2 cup cold water, bring to a boil, and cook uncovered, stirring occasionally, until the water has evaporated and the broccoli is tender-crisp, about 3–4 minutes.
Return the cooked chicken to the pan with the broccoli.
Add the cold cooked Hokkien noodles directly to the pan and spread gently; it’s okay if they stick together at first.
Whisk the 1/4 teaspoon cornstarch into the reserved sauce in the measuring cup until smooth, then pour the sauce over the noodles, chicken, and broccoli.
Bring the sauce to a full boil in the pan so it thickens and coats the noodles, then remove from heat.
Sprinkle the chopped mint leaves over the stir-fry and serve immediately.