Make the peanut sauce: whisk together peanut butter, soy sauce, rice vinegar, sesame oil, chili garlic sauce, garlic, ginger, and honey in a bowl until smooth.
Thin the sauce with water, adding 1 tablespoon at a time, until it reaches your desired consistency.
Heat canola oil in a large sauté pan over medium-high heat.
Season the chicken pieces with salt and pepper, then add to the hot pan. Let sit undisturbed a few minutes until browned, then turn to brown the other side and cook until cooked through, about 6–8 minutes total depending on size.
Add broccoli to the pan and cover with a lid; steam until bright green and tender, about 3–4 minutes.
Turn off the heat, pour the peanut sauce over the chicken and broccoli, and stir to coat everything evenly.
Serve immediately over rice or cauliflower rice if desired.