1. Melt the butter in a large pan.
2. Add the leeks and thyme and cook for a few minutes until softened, stirring regularly.
3. Then cover the pan and gently fry for 15-20 minutes until completely cooked down and tender, stirring occasionally.
4. Meanwhile, cook the potatoes in a pan of boiling salted water for 10-12 minutes until nearly tender.
5. Add the broccoli stems and cook for another 5 minutes, then add the florets and simmer for a further 3 minutes until just tender.
6. Drain the potato mixture and place in a food processor with the leeks- you may have to do this in batches.
7. Blend until smooth and then return to a clean pan.
8. Stir in the cream, season to taste and re-heat gently just before serving.