In a small bowl, mix together the shrimp and cornstarch. Heat a large skillet or wok over medium-high heat. Add 1 tablespoon of oil to skillet and swirl it around, coating the pan. Stir-fry shrimp for 4 minutes, then remove and set aside.
Add another tablespoon of oil to the same pan. Chop green onions, grate ginger, and mince garlic; add to pan. Stir-fry for 30 seconds and then and to the shrimp on the side.
Add broth and rice to the pan and bring to boil; chop broccoli and add to the pan once liquid is boiling. Turn heat down, cover, and simmer 20-25 minutes until rice is tender and liquid has absorbed. If the liquid evaporates too quickly, add a bit of water or more broth 1 tablespoon at a time.
Add in soy sauce, vinegar, and honey, along with the shrimp and onions. Stir to combine and heat through.
Top each serving with a bit of pineapple, or serve as a side.