To make the gnocchi, combine the milk with the chopped vegetables, 1 teaspoon of thyme and bay leaf and gently simmer for 10 minutes to infuse all the flavour. Then pass the milk through a sieve into pot and return to the heat. Simmer again and then whisk in the semolina and stir until thick. Continue to stir for about 5 minutes and then remove from the heat.
While still hot whisk in the egg yolks and ½ the grated Parmesan and season with salt and pepper to taste. Line a flat baking tray with baking paper and then spread the thick
semolina over the tray so that it is about 2-3cm thick. Then allow it to cool.
Once cool, cut the gnocchi dough into circles using a round pastry cutter, reforming any trim so as to use all the semolina. Rub a baking dish with butter and then arrange the semolina gnocchi slightly overlapping. Dot the top of the gnocchi with half the butter and more Parmesan cheese. Place the baking dish into a medium hot oven and bake until golden brown.
While the gnocchi bakes, melt the remaining butter in a saucepan and add the garlic and thyme. Then add the mushrooms and sauté until the mushrooms soften. Then add the cream, salt and pepper and simmer to slightly thicken. Finally add the chopped parsley and a good squeeze of lemon juice.
Once the gnocchi is out of the oven pour the mushroom sauce over the gnocchi and finish with a grating of Parmesan cheese.