In a small bowl, whisk together 3 tablespoons of honey, 3 tablespoons of soy sauce, 2 cloves of minced garlic, and 1 teaspoon of freshly grated ginger. Set aside.
Heat 1 tablespoon of olive oil in a large skillet over medium-high heat. Add 2 cups of broccoli florets, season with salt and pepper, and sauté for 4-5 minutes until bright green and slightly tender but still crisp. Remove broccoli and set aside.
In the same skillet, add more olive oil if needed, then add 1 pound of peeled and deveined shrimp. Season with salt and pepper. Cook shrimp for 2-3 minutes on each side until pink and opaque.
Pour the honey-garlic sauce over the shrimp in the skillet. Toss to coat evenly and cook for another 2 minutes until the sauce thickens and glazes the shrimp.
Return the sautéed broccoli to the skillet. Toss gently to coat shrimp and broccoli in the sauce.
Spoon 1 cup of cooked rice into each bowl. Top with the shrimp and broccoli mixture. Garnish with sesame seeds and sliced green onions.
