Rinse quinoa under hot water and cook in vegetable stock for 18-20 minutes. At the end of the cooking time, cool in an open saucepan. Finely grate the Parmesan cheese.
In the meantime, finely dice 1 shallot and sauté with clove and bay leaf in 20 g butter until colorless. Fold in flour and sauté for 5-6 min. at low temperature without color. Add 350 ml of milk and bring to a boil while stirring throughout. Add remaining milk, bring to boil repeatedly while stirring. Season with sugar, pepper, salt and nutmeg. Add mustard and simmer sauce for 40-50 min. at low heat to 500 ml, stirring occasionally.
Halve the remaining shallots. Clean carrots, remove peel, cut in half lengthwise and cut diagonally into 3-4 cm pieces. Remove peel from buttered turnip, celery and potatoes, cut into 3-4 cm pieces. Grease a gratin dish with the remaining butter. Spread the prepared vegetables evenly in it and fill up with the béchamel sauce. Cook the casserole in the heated oven at 180 degrees (gas 2 3, convection oven not recommended) for 60-70 min.
Loosen the quinoa with a fork, mix it with the cheese and spread it evenly on the casserole 5 minutes before the end of the cooking time. Turn on the oven grill and bake the casserole until golden brown.