Begin by cooking the rice according to package instructions. Once cooked, set aside and keep warm.
In a large skillet or wok, heat 1 tablespoon of vegetable oil over medium-high heat.
Add the minced garlic and sauté for about 30 seconds until fragrant, being careful not to burn it.
Increase the heat to high and add the ground beef. Break it apart with a spatula and cook until browned, about 5-7 minutes. Drain excess fat if necessary.
Stir in the soy sauce, chili paste, hoisin sauce, rice vinegar, sesame oil, and brown sugar. Mix well to combine all the flavors.
Add the broccoli florets and snap peas (or green beans) to the skillet. Stir-fry for an additional 3-4 minutes until the vegetables are tender but still crisp.
Taste the stir-fry and adjust the spice level by adding more chili paste or crushed red pepper flakes if desired.
Serve the spicy ground beef and garlic veggies over a bed of warm rice. Garnish with sesame seeds before serving.