To make gnocchi; bring a large pot of water to the boil and cook potatoes until tender when pierced with a skewer. Drain. Return potatoes to pot and shake over a low heat for 2 minutes to remove excess moisture.
Push potatoes through a potato ricer or a coarse sieve. Allow to cool for 10 minutes. Add egg yolks, sifted flour, parmesan and salt. Stir with a wooden spoon until mixture forms a dough. Use your hand to bring together. Turn out onto a floured surface and knead lightly until smooth.
Roll dough into a 30cm log. Cut into 6 even pieces. Roll each piece into a 35cm x 2.5cm rope. Cut rope into 2cm pillows with a sharp knife. Use a fork to press down gently on cut edge of each pillow to make gnocchi shape. Transfer to a tray in a single layer. You can freeze gnocchi at this stage if making ahead of time.
Bring a large saucepan of water to a gentle boil. Cook gnocchi in four separate batches for 2½-3 minutes each or until it floats to the surface. Remove with a slotted spoon and place on a tray. Cover to keep warm.
To make mushrooms; heat half of the butter and half of the oil in a large, deep frying pan over a medium-high heat. Add Swiss and button mushrooms and cook, stirring for about 5-6 minutes or until soft and lightly golden. Add half of the wine and lemon thyme and cook for 1 minute. Transfer to a bowl and cover to keep warm.
Heat remaining butter and oil in pan. Add speck and pine mushrooms. Cook, stirring for 5 minutes. Add chestnut mushrooms (if using) and cook for 2 minutes until soft. Add remaining wine, season and cook for 1 minute.
Return pan to a medium heat and add half of the gnocchi. If gnocchi sticks to pan, add a little oil. Cook, stirring for 2 minutes. Add ½ of mushroom mixture and stir to heat through. Remove from pan, set aside and keep warm. Repeat with remaining gnocchi and mushroom mixture. Serve with pecorino and thyme sprigs.