Steam broccoli until desired tenderness is reached. It should take about 5-6 minutes on the stove, or 2-4 minutes in the microwave.
Stovetop steaming: Fill a saucepan with 1-2 inches of water and place a steamer basket on the bottom. Bring water to a boil, then add broccoli to steamer basket. Reduce heat to medium and steam 5-6 minutes until tender.
Microwave steaming: Place broccoli in a bowl and add a splash of water. Cover and microwave for 2-4 minutes until broccoli reaches your desired tenderness. (I use a Lekue* for quick and easy steaming of veggies.)
Place broccoli in a large bowl and set aside to cool while you prepare the sesame sauce.
Grind toasted sesame seeds. (Typically with a pestle and mortar, but you can try using a coffee/spice grinder, food processor, or blender. You may need to double or triple the quantity.)
Add sugar and soy sauce and mix in with the ground sesame seeds.
Add water as needed to make the sauce easier to mix with the broccoli.
Add sesame sauce to broccoli and mix well until broccoli is evenly coated.