Make the sauce: In a bowl, whisk peanut butter, soy sauce, rice vinegar, lime juice, honey, and sriracha. Add 1/3 cup coconut milk (or water) and whisk until smooth.
Thin with more liquid until pourable but still creamy. Set aside.
Prep the chicken: Pat the chicken dry and slice it thinly against the grain. Season lightly with salt and pepper.
Cook the broccoli: Heat 1 tablespoon oil in a large skillet or wok over medium-high heat.
Add broccoli and a pinch of salt. Stir-fry 3–4 minutes until bright green and crisp-tender. Transfer to a plate.
Sear the chicken: Add the remaining 1 tablespoon oil to the pan.
Add chicken in an even layer. Cook 4–6 minutes, stirring occasionally, until just cooked through and lightly browned.
Add aromatics: Reduce heat to medium. Stir in garlic and ginger.
Cook 30–60 seconds until fragrant, being careful not to burn.
Sauce it up: Return broccoli to the pan. Pour in the peanut sauce. Toss everything to coat.
Simmer 1–2 minutes, adding a splash of water if it’s too thick. Taste and adjust with more lime, soy, or honey.
Finish and garnish: Stir in sesame oil if using. Top with green onions and chopped peanuts.
Serve: Spoon over rice or noodles.
Add lime wedges and cilantro if you like.