Cook the jasmine rice according to package directions.
When the rice is nearly done, heat 1 tablespoon olive oil in a large skillet over medium-high heat.
Add grated ginger and minced garlic to the skillet and cook, stirring constantly, about 1 minute until fragrant.
Stir in the hoisin sauce and soy sauce and mix until combined.
Add the broccoli florets, cover the skillet, and cook for 4 minutes until the broccoli is tender-crisp.
Add the shrimp, stir to coat with the sauce, then cover and cook 3 minutes or until the shrimp are pink and cooked through.
Serve the shrimp and broccoli over the cooked rice and garnish with sesame seeds and sliced scallions to taste.