Prepare the chicken: Slice thick chicken breasts horizontally into thinner, evenly sized pieces. Pat them dry before adding the marinade.
Make the marinade: Whisk pineapple juice, soy sauce, brown sugar, rice vinegar, ginger, garlic, ketchup, lime juice, and optional Sriracha until combined.
Reserve the sauce: Remove ½ cup of the marinade before adding the chicken and keep it separately refrigerated. This portion will become the finishing sauce.
Marinate the chicken: Add the chicken to the remaining marinade, cover, and refrigerate for 2–4 hours.
Heat the grill: Preheat a grill or grill pan over medium-high heat and lightly oil the surface if needed.
Grill the chicken: Remove excess marinade from the chicken and place it on the hot grill. Cook until browned on both sides and the thickest part reaches 165°F (74°C).
Rest the chicken: Transfer the cooked chicken to a clean plate and let it rest for a few minutes before slicing.
Grill the pineapple: Place pineapple chunks on the hot grill and cook until they develop golden-brown caramelized edges, turning once or twice.
Prepare the sauce: Pour the reserved marinade into a small saucepan and bring it to a proper boil. Mix cornstarch with water, whisk it into the boiling sauce, and cook until lightly thickened and glossy.
Warm the sides: Prepare the jasmine rice and baby broccoli while the chicken and pineapple finish cooking.
Assemble the plate: Add jasmine rice and baby broccoli to each plate, then arrange sliced grilled chicken and caramelized pineapple alongside them.
Add the sauce: Spoon a moderate amount of sweet soy ginger sauce over the chicken rather than covering the entire plate.
Finish and serve: Garnish with sliced green onions, sesame seeds, and a lime wedge if desired.