Rinse brown rice under cold water and combine with 2 cups water in a pot. Bring to a boil, then reduce heat to low, cover, and simmer for 40-45 minutes until tender.
While rice cooks, heat 1 tablespoon olive oil in a large skillet or wok over medium-high heat.
Add shrimp and season with salt and pepper. Cook for 2-3 minutes per side until pink and opaque. Remove and set aside.
In the same skillet, add remaining olive oil and sauté garlic and ginger until fragrant, about 1 minute.
Add bell pepper, snap peas, carrot, and broccoli. Stir-fry for 4-5 minutes until veggies are crisp-tender.
In a small bowl, whisk together soy sauce, honey, sesame oil, and red pepper flakes.
Return shrimp to the skillet and pour the sauce over the mixture. Toss to coat and cook for another 2 minutes.
Serve the shrimp stir-fry over cooked brown rice. Garnish with chopped green onions and toasted sesame seeds.