Start by making the filling. Heat the oil in a pan on low heat. Add mushrooms, garlic and thyme. Season to taste with salt and pepper and cook for 4-5 minutes, until the mushrooms are browned and have released their liquid. Tip them into a sieve set over a bowl to drain and leave to cool. Reserve the liquid.
Make the gnocchi. Boil the potatoes in salt water until tender. Drain and mash them until they're smooth and creamy with no lumps. Season with salt and pepper.
Mix the flour into the warm potatoes. Tip out the mixture onto a very light floured surface (you want to add as little extra flour as possible) and knead together to form a dough. Roll out to about 4mm thick with a rolling pin, and using n 8cm pastry cutter (or glass), cut out discs, rerolling the dough when necessary. You should get about 20 discs.
Place a small amount (about a teaspoon) of the mushroom mixture onto each disc and then gather up the edges over the filling and press together to form balls.
Bring a saucepan of salted water to a boil. Add the gnocchi a few at a time and leave for 4-6 minutes, until you have cooked out the flour and they are heated through. They will rise to the surface when they are ready. Remove them gently one by one, with a slotted spoon and set aside to drain on a kitchen paper (you can also let them drain in a colander placed over a sink).
Heat the butter in a pan over a medium heat. If you want browned butter, heat until the butter starts browning and then add gnocchi and sage in batches. Cook for 3-4minutes, turning gently to brown them on all sides.
Serve immediately.