In a large saucepan, heat the sesame oil over medium heat. Add the garlic, green onions, and ginger; cook and stir for 1 minutes.
Add the broccoli and 1 cup of the water. Increase heat to medium-high, cover, and cook for 1 minute.
Add the spinach, re-cover, and cook 1 minute longer or until spinach is just wilted. Remove pan from heat and let stand, covered, for 5 minutes.
Transfer the contents of the pan, along with 1 cup remaining water, to a blender. Puree until smooth, then return mixture to pan.
Whisk the remaining water, salt, lemon juice, and sriracha into the soup (add more water if too thick). Reheat over medium-low heat until hot, about 5 minutes. Adjust the salt and pepper to taste.
If desired, serve sprinkled with sesame seeds and drizzled with extra sriracha.