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Heat the oil in a wide, shallow ovenproof pan set over a medium heat. Cook the onions until starting to caramelise, about 10 mins. Tip in the carrots and mushrooms, and cook for another 5 mins until the mushrooms have softened a little. Stir in the tomato purée.
Tip in the root veg, half the thyme and all the pearl barley, and stir well. Crumble in the veg stock cube and add the bay, soy sauce, mustard and vinegar. Season and pour in 600ml water. Bring to a gentle simmer, cover with a lid and cook for 10 mins.
Meanwhile, prepare the veg for the topping. Slice the potatoes, beetroot and sweet potatoes as thinly as you can – use a mandoline if you have one. Beetroot will stain your hands, so use kitchen gloves, if you like. Melt the butter in a pan over a low heat and mix with the honey, remaining thyme and a grind of black pepper.
Remove the pan from the heat. Arrange the sliced vegetables on top of the dish in concentric circles, overlapping potato, sweet potato and beetroot slices until the whole dish is covered. Brush the butter and honey mixture over the top, making sure every slice is covered. Season well with salt. Will keep chilled overnight or wrapped and frozen for up to three months. Leave to cool completely first. Defrost overnight before continuing with step five.
Heat the oven to 180C/160C fan/gas 4. Cover the pan with a lid or piece of foil and bake for 20 mins. Uncover the dish and cook for a further 30 mins until the topping is crispy and the potatoes are golden.