Clean and grate the mushrooms. Peel and finely chop the onions. Heat 2 tablespoons of oil in a saucepan. Brown the mushrooms in it. Add onions, fry briefly, add stock and cream.
Bring everything to the boil and simmer for 5 minutes. Add sauce thickener and bring to the boil. Wash thyme, dab dry and, except for a little garnish, pluck from the stalks, chop coarsely and add to the mushrooms.
Season to taste with salt and pepper. Mix eggs and milk. Add parmesan and 1 pinch of salt. Slice bread diagonally and turn in the egg milk. Heat the rest of the oil and fry the slices of bread on both sides.
Arrange the mushroom ragout on a plate together with the French toast. Serve garnished with remaining thyme.