Begin by washing the jasmine rice under cold water until the water runs clear. In a medium pot, combine the rice with 2 cups of water, bring to a boil, then lower the heat, cover, and simmer for about 15 minutes or until the water is absorbed. Remove from heat and let it sit covered for 5 minutes. Fluff with a fork before serving.
In a large bowl, mix together the honey, soy sauce, minced garlic, and grated ginger. Add the shrimp to the bowl and toss well to coat. Let it marinate for about 15 minutes while you prepare your vegetables.
In a large skillet or wok, heat 1 tablespoon of olive oil over medium-high heat. Add the broccoli, sliced bell pepper, and julienned carrot. Stir-fry the vegetables for about 5-7 minutes until they are tender but still crisp. Season slightly with salt and pepper. Remove the vegetables from the skillet and set aside.
In the same skillet, add the remaining tablespoon of olive oil. Once hot, add the marinated shrimp including the marinade. Cook for about 3-5 minutes until the shrimp are pink and cooked through, stirring occasionally.
Divide the cooked jasmine rice into serving bowls. Top each bowl with the sautéed vegetables and a generous serving of honey garlic shrimp. Drizzle any remaining sauce from the skillet over the top.
Sprinkle sesame seeds and chopped green onions over each bowl for added flavor and crunch.