Rinse the quinoa and drain it. In a saucepan bring 50 cl of broth to a boil. Add the quinoa. Bring to a boil again and cook for 10 minutes uncovered. Cover and reserve for 20 minutes off heat.
Peel the onion and garlic clove. Chop it finely. Heat 2 tbsp of olive oil in a large pan, then sauté the onion and garlic for 3-4 minutes over high heat. Reserve in a bowl.
Add quinoa, breadcrumbs, cottage cheese, egg yolk, almonds, salt and pepper to the bowl and mix well. Form balls with this preparation. Flatten them slightly and reserve.
Peel the potatoes, cut them into pieces. Cook in a saucepan of lightly salted boiling water for 15-20 minutes (cold start).
Meanwhile, cut the chestnuts in 3-4 pieces. Caramelize them in a pan with 10 g of butter. Reserve.
Rinse the basil leaves and chop them roughly. Peel the shallots and chop them finely. Sauté in a saucepan with 20 g of butter, 2-3 minutes over high heat. Pour 20 cl of milk and the remaining broth. Bring to a boil while whisking. Remove from heat, add the nutmeg, parmesan cheese, salt, pepper and add the basil, mix in a blender. Keep warm.
Drain the potatoes and mash them. Boil the rest of the milk with the remaining butter in a saucepan. Pour the mashed potato. Mix well, add salt and pepper and the chestnuts and mix.
Heat the remaining oil in a frying pan and cook the patties on each side. Serve them with the mashed potato and basil sauce.
