Heat oil in a large pan over medium-high heat. Add broccoli and stir. Make space in the center and add ginger and garlic with a bit more oil. Sauté until fragrant, then mix with broccoli.
Pour the sauce mixture into the pan with broccoli. Simmer, reduce heat, cover, and cook until broccoli is tender. Remove broccoli and reduce the sauce. Toss broccoli back in with sesame seeds.