1. Preheat your oven to 230℃ fan. 
2. Put the dried mushrooms into a bowl and pour over the boiling stock. Leave them to soak for 30 minutes. 
3. In a food processor, finely chop the fresh mushrooms (or do this by hand) and toss them in 2 tablespoons of olive oil and ½ teaspoon of salt, then spread them out onto a large baking tray and cook for 30 minutes (if you are concerned that the mushrooms will stick to your baking tray, you can line it with baking parchment first), giving a good stir twice during cooking, until the mushrooms are cooked thoroughly and evenly. Remove from the oven and reduce the oven temperature to 200℃ fan. 
4. While the mushrooms are roasting, finely chop the onion, garlic and carrot in the food processor (or by hand). Heat the remaining olive oil in a large frying pan or saucepan on a medium-high heat - once hot, add the onion, garlic and carrot with ¾ teaspoon of salt and about 10 grinds of black pepper and fry for 10 minutes, stirring occasionally, until soft and golden. 
5. If using a food processor, tip in the dried mushrooms along with the stock they have been soaking in and blitz until they’re roughly chopped. (If you are doing this by hand, strain the liquid through a sieve into another bowl, squeezing the mushrooms to get out as much liquid as possible. Keep the liquid and roughly chop the rehydrated mushrooms). 
6. Add the tomato purée to the pan, cook for 1 minute, then add the tin of tomatoes and the rehydrated mushrooms (and their liquid) and cook for another 6 minutes, stirring occasionally. 
7. Add the roasted mushrooms and cook over a medium heat, uncovered, for 5 minutes without stirring. Then add 250ml boiling water, stir and bring the sauce to a simmer. Cook, still uncovered, for a further 20 minutes, stirring occasionally, until you have a lovely, thick sauce. Stir in the spinach and half the cream, stir and cook for another 2 minutes, then remove from the heat. 
8. To assemble the lasagne: lightly grease the inside of an ovenproof dish (about 25 x 30cm) with light olive oil. Combine the Comté with the chopped herbs in a bowl. Spread a quarter of the ragu over the bottom of the lasagne dish, then sprinkle over a quarter of the Comté and herb mixture and then a layer of pasta. Repeat these layers twice, then finish with a final layer of sauce and Comté sprinkled on top - you will have four layers of ragu, four layers of Comté and three layers of pasta. Finally, drizzle over half the remaining cream and 1 tablespoon extra virgin olive oil, then cover the dish with foil.* 
9. Bake the lasagne the centre of the oven for 15 minutes. Remove the foil, turn the dish around and bake for another 15 minutes until the lasagne is bubbling hot. Remove the lasagne from the oven and leave it for 5 minutes before drizzling over the remaining extra virgin olive oil and double cream and scattering over a few small or torn basil leaves. 

* If you are making your lasagne in advance, you can let it cool down and cover it with the foil then refrigerate it at this point. This can be done a day or two before you bake it. Just remember to bring it up to room temperature before it goes in the oven and add an extra 5 to 10 minutes to the initial cooking time (when it is covered with the foil and cooking at 200℃).