Heat a large skillet over medium-high heat. Add the 1 pound 90% lean ground beef and the 3 minced garlic cloves. Cook, breaking the beef into crumbles, until no longer pink, about 4–6 minutes.
Transfer the cooked beef to a plate and set aside. Carefully drain and discard excess grease from the skillet.
Return the skillet to medium-high heat and add the 1 tablespoon olive oil. Add the 1 diced red bell pepper, 1 sliced zucchini, ½ cup sugar snap peas, ½ cup shredded carrots, and 8 ounces sliced mushrooms. Sauté, stirring occasionally, until the vegetables are tender-crisp, about 3–5 minutes.
Add the reserved ground beef back to the skillet with the vegetables and stir to combine.
In a small bowl, whisk together ½ cup packed light brown sugar, ½ cup reduced-sodium soy sauce, 1 tablespoon sesame oil, ½ teaspoon ground ginger, ¼ teaspoon crushed red pepper flakes, and ½ teaspoon pepper. Pour the sauce over the beef and vegetables, bring to a simmer, and cook 1–2 minutes more so the sauce warms and coats the mixture.
Serve the stir fry over 2 cups cooked white rice and top with sliced green onions and sesame seeds as garnish.