Peel and finely chop the onion. Peel and crush or finely grate the garlic clove. Trim the root from the broccoli and cut into small florets. Slice the stalk into small pieces.
Pour 1 tbsp oil into a pan and bring to a medium heat. Slide in the onion and sprinkle in a little salt and pepper. Fry for 4-5 mins, stirring occasionally, till softened. Stir in the garlic and cook for a further min.
Tip the broccoli into the pan and cover with 750ml boiling water. Crumble in the stock cube and stir well to combine. Bring the water back to the boil, then simmer for 5-6 mins, till the broccoli is tender.
Meanwhile, set a dry frying pan on a medium-high heat. Toss in the sunflower seeds and cook for 3-4 mins, shaking and turning occasionally, till the seeds are golden on all sides. Slide into a small bowl and set aside.
Swirl the tahini into the pan. Use a stick blender to whizz the broccoli into a smooth soup. No stick blender? No problem, simply transfer the contents of the pan (in batches if necessary) and blend. Squeeze in half of the lemon juice and have a taste. Add a little more salt and pepper if needed.
Ladle the soup into bowls. Scatter over the toasted seeds and serve.