Three-bean shepherd's pie

Name: Three-bean shepherd's pie
Prep time: 30 min
Cook time: 26 h
Total time: 26 h
Yield: 6 portions
Ingredients: 80 g dried chickpeas; 80 g dried borlotti beans; 80 g dried kidney beans; 1000 g water; 130 g water; 20 g dried shiitake mushrooms; 2 garlic cloves; &frac18; tsp asafoetida; 1 brown onion; 20 g unsalted butter; 6 sprigs fresh flat-leaf parsley; 170 g tomatoes; 200 g zucchini; 70 g celery stalks; 150 g potatoes; 120 g carrot; 2 tbsp Vegetable stock paste; 2 tsp dried thyme; 1 tsp salt; 1 tsp ground black pepper; 60 g red wine; 50 g tomato paste; 100 g fresh field mushrooms; 50 g Parmesan cheese; 250 g full cream milk; &frac18; tsp sea salt; &frac18; tsp ground black pepper; 1000 g sweet potato; 30 g unsalted butter; sea salt