Put a kettle on to boil. Put the dried mushrooms into a heatproof bowl, cover with boiling water and leave them to soak for 30 minutes.
Meanwhile, heat the olive oil in a large saucepan over a medium-high heat. Add the garlic and stir-fry for 15 seconds, then add the fresh mushrooms and continue stir-frying for 10 minutes, or until they have wilted.
Strain the soaking liquid off the wild mushrooms through a fine sieve lined with muslin or kitchen paper, and add 50 ml (2 fl oz) of it to the cooked mushrooms.
Roughly chop the rehydrated wild mushrooms and add them to the pan with the tomato purée, thyme, wine and brandy. Season to taste and simmer, covered, for 20 minutes, or until you have a thin, richly flavoured sauce.
Meanwhile, put the polenta and salt into a large saucepan and pour in 1.4 litres (2 pints 10 fl oz) of water, whisking continuously to prevent any lumps. Bring the mixture to the boil, then simmer for 10 minutes, stirring frequently until it becomes firm but not stiff.
Arrange spoonfuls of the polenta on individual plates, spoon the mushroom sauce alongside and garnish with the parsley and thyme.