Heat a large skillet over medium-high heat. Add the ground beef and cook, breaking it up with a spatula, until browned and cooked through, about 5–7 minutes. Drain excess fat if necessary and set the beef aside.
In the same skillet, melt 2 tablespoons of butter over medium heat. Add the minced garlic and sauté for 1–2 minutes until fragrant. Stir in the honey, soy sauce, and sesame oil (if using). Let it simmer for 1–2 minutes to combine the flavors.
Add the uncooked rice to the skillet with the sauce and stir to coat. Pour in the beef broth, stir well, and bring to a gentle boil. Reduce the heat to low, cover the skillet with a lid, and let the rice simmer for 15–18 minutes, or until the rice is tender and the liquid is absorbed.
Stir in the frozen peas (or mixed vegetables) and the cooked ground beef. Cook for an additional 2–3 minutes, or until the vegetables are heated through. Taste and adjust seasoning with salt and pepper, if needed.
Stir in the remaining tablespoon of butter for a rich, creamy finish. Garnish with sliced green onions and sesame seeds, and serve warm.