You will need a 22cm tart tin with a removable base.To make the pastry, cut the butter into cubes and rub it into the flour with your fingertips until it resembles coarse breadcrumbs.
Mix in the egg yolk and parmesan, bringing the ingredients together into a firm ball of dough, adding a tablespoon or two of cold water if necessary. You can do this in seconds using a food processor.
Tip the dough on to a lightly floured board and knead for 30 seconds or so (no longer) shaping it into a ball as you go. Wrap in clingfilm or greaseproof paper and chill in the fridge for 30 minutes.
While the dough chills, make the filling. Pour the cream into a medium-sized saucepan, add the parmesan rind and bring to the boil. Remove the cream from the heat immediately when it starts to boil, then cover with a lid and set aside.
Cut the mushrooms into small pieces. In a small frying pan, warm the oil then fry the mushrooms for 4 or 5 minutes, until slightly sticky. Chop the dill and toss with the mushrooms and set aside.
Remove the dough from the fridge and tenderly roll into a disc large enough to line the tart case. Press the pastry into the edges, patching it where necessary. Make certain there are no tears or holes.
Chill for 20 minutes, allowing the pastry to relax. Set the oven at 180C fan/gas mark 6 and place an upturned baking sheet on the middle shelf to heat up.
Place a sheet of baking paper or foil on top of the pastry, fill with baking beans and slide into the preheated oven on top of the warm baking sheet.
Bake for 25 minutes, then carefully remove the parchment and beans and return to the oven for a further 5 minutes until dry to the touch. Lower the heat to 160C fan/gas mark 4.
Break the eggs into a bowl and beat gently, then add the cream (removing the parmesan rind). Season with salt and pepper, add the fried mushrooms, then spoon into the tart case and bake for 25 minutes.