Rinse the brown rice under cold water until the water runs clear.
In a medium saucepan, combine the rinsed brown rice and 2 cups of water. Bring to a boil over high heat.
Once boiling, reduce heat to low, cover, and simmer for 40 minutes or until rice is tender and water is absorbed. Remove from heat and let it sit covered for 5 minutes.
While the rice cooks, heat olive oil in a large skillet over medium-high heat.
Add the chopped onion and cook for 3 minutes until softened.
Add the minced garlic and cook for 1 minute until fragrant.
Add the ground beef to the skillet. Cook, breaking it apart with a spatula, until browned and cooked through, about 6-8 minutes.
Drain any excess fat from the skillet.
Add the diced red bell pepper, broccoli florets, and shredded carrots to the beef. Cook for 5 minutes until vegetables are tender-crisp.
In a small bowl, whisk together soy sauce, rice vinegar, black pepper, salt, smoked paprika, and crushed red pepper flakes.
Pour the sauce mixture over the beef and vegetables. Stir well to combine and cook for an additional 2 minutes to heat through.
Fluff the cooked brown rice with a fork and divide it evenly among four bowls.
Top each bowl of rice with the beef and vegetable mixture.
Garnish with sliced green onions and sesame seeds before serving.