Traditionally carpaccio is served raw, but I'm searing my beef to give it colour and make it a bit ragged. I've gone heavy on the rosemary here because it goes beautifully with beef: they're like Romeo and Juliet - completely in love. This will make a really sophisticated starter, a great lunch or even a killer snack.
Preheat your oven to 375 degrees F/ 190 degrees C/ Gas 5. Wash your squash then carefully cut it in 1/2. Scoop out the seeds then pick through them and put some of the nicest ones in a small pan with a lug of olive oil. Get rid of the others and any stringy flesh.
Fry the seeds until golden, then remove from the heat and keep to one side.
Cut your squash halves into thin wedges and arrange in a roasting tray. In a pestle and mortar, bash up the fennel, coriander seeds, dried chile, oregano with 1 teaspoon salt and a pinch of pepper until fine. Tip these spices all over the squash then sprinkle over the cinnamon. Crumble the chestnuts directly into the tray, then drizzle with just enough olive oil to coat everything. Toss everything together with your hands then pop in the hot oven to cook for 40 to 45 minutes until beautiful, golden, and soft when you pinch it.
Take the squash out of the oven and sprinkle over a pinch of salt from a height. Carefully tip the golden seeds into the tray, leaving the oil behind in the pan. Put your rosemary leaves on a board with a good pinch of salt and pepper and finely chop them. Roll your beef around on the board until it is well coated in the rosemary. Return your pan of oil to a high heat, and once it is screaming hot, add the beef. Sear it for about 1 minute to 1 minute 30 seconds so it browns, then turn it over and do the same on the other side.
Meanwhile, make your dressing. Add the mustard, extra-virgin olive oil and lemon juice to a bowl and mix well. Have a taste and check the seasoning then put aside.
Use a really sharp knife to slice the beef up as thinly as you can without hacking it up or ruining it! Go thicker to do it nicely if you need to. Carefully, push the flat blade of a knife over each slice of beef, flattening it so it spreads out more. Arrange the slices on a large platter and sprinkle over a pinch of salt (the seasoning won't have flavoured the centre of the beef).
Arrange the roasted squash over the top, then scatter over any roasted chestnuts and toasted seeds left behind in the roasting tray. Drizzle over that wonderful dressing, then lightly dress your salad leaves and pop them on top. Take it to the table with a block of Parmesan for shaving over and let everyone can help themselves.
Remember you're searing the beef to get a bit of colour on the outside, not cooking it - it should be blue in the middle.