Heat the olive oil gently in a 35cm/14in paella pan or a large frying pan. Add the onion and fennel and fry, stirring, over a gentle heat for 3-4 minutes.
Add the mushrooms and garlic, and cook until the juices begin to run, then increase the heat to evaporate the juices. Push the onion and mushrooms to one side. Add the chicken pieces and fry briefly.
Stir in the rice, pour in the stock, then stir in the saffron, thyme, butter beans and peas. Bring to a simmer and then cook gently for 15 minutes without stirring.
Remove from the heat and cover the surface of the paella with a circle of oiled greaseproof paper. Cover the paper with a clean dish towel and leave for about 5 minutes before serving the paella.
For a vegetarian mushroom paella, omit the chicken, replace the chicken stock with vegetable stock and, if you can, include chicken of the woods in your choice of mushrooms.