Heat your oven to 200°C/Fan 180°C/Gas 6. Pop the porcini into a small heatproof bowl and cover with 125ml boiling water. Leave to soak for 10 mins.
Peel and finely slice the onion. Heat 1 tbsp olive oil in an ovenproof frying pan over a medium-high heat (see our tip for what to do if you don't have an ovenproof pan). Add the onion and lower the heat. Cook for 5 mins, stirring occasionally, till the onion is tender and glossy.
Peel and grate the garlic. Finely slice the chestnut mushrooms. Add the mushrooms to the onion. Season. Cook over medium-high heat for around 5 mins or till the mushrooms are glossy and juicy. Add the garlic for the final 1 min of cooking.
Add the porcini and their soaking liquid to the pan. Cook and stir for 1-2 mins. Take off the heat. Stir the crème fraîche and 2 tsp mustard through the mushrooms. Season to taste.
Finely chop the dill, leaves and stalks. Peel and coarsely grate the potatoes into a large bowl. Add half the dill. Season. Pour in 1 tbsp oil and turn to mix. Scatter the mix over the mushrooms. Pop in the oven on a high shelf. Bake for 30 mins, or till the potatoes are golden and crisp.
While the pie bakes, grate the zest from the lemon. Juice it. Pop the zest in a large bowl. Whisk in the juice from half the lemon, 2 tbsp olive oil and a pinch of salt. Set aside. Peel the beetroot. Thinly slice it. Fold the beetroot through the dressing. Put to one side.
When the pie is ready, pile the lamb's lettuce on 2 warm plates and scatter over the beetroot, drizzling over any dressing from the bowl. Serve the pie garnished with the rest of the dill.