Add oil to a medium-sized pan and heat on almost high till the oil shimmers. Turn heat to medium. Add ginger and garlic, saute gently for a minute or so. Add the sauce and stir and cook for a couple of minutes.
Once the smell of the mixture changes - it will brown and caramelize a little - add in the broccoli and toss it all together. Coat the florets and leaves (if any) in the sauce mixture Cook for 10 minutes on medium heat. Optional: depending on how the broccoli is cooking you may need a couple of tbsp of water. Add sesame seeds and toss and turn. Add salt as needed. Optional: if you're adding cooked tofu double the sauce and add in a few minutes after the broccoli.
Serve with lime wedges, crushed nuts on top along side salmon or rice