Add the dried mushrooms to the hot stock and leave to infuse. Heat 1 tbsp oil in a large casserole dish. Add the chestnut mushrooms and fry for 4-5 minutes until golden. Remove from the pan.
Add the remaining oil and fry the shallots and carrots for 8-10 minutes until starting to soften. Add the garlic, thyme and tomato purée and cook for a further 1 minute. Return the chestnut mushrooms to the pan with 1 tbsp flour and cook for 1 minute. Add the burgundy, vegetable stock and dried mushrooms. Bring to the boil, then simmer for 20 minutes.
Mix the remaining flour with the butter and add to the sauce. Continue to simmer for 10 minutes until the sauce is thick and glossy. Season well.
Meanwhile, put the celeriac and garlic in a large saucepan and cover with the milk. Bring to the boil and simmer for 15 minutes until the celeriac is soft. Drain, reserving the milk. Return the celeriac to the pan and add 100ml of the reserved milk and the mustard. Mash. Serve the mash with the bourguignon on top.