To make the pasta, tip the flour onto a work surface and make a well in the middle. Break the eggs into the well and mix the flour with a fork until everything is combined. Gather the mixture together into a lump and knead until smooth and elastic. Wrap in cling film and chill in the fridge for 30 minutes.
While the pasta is chilling, mix all the ingredients for the spice blend and set aside.
To make the lamb sauce, heat the oil in a large saucepan and fry the onions and carrot with a pinch of salt for 8–10 minutes, or until softened. Add the mince, spice blend and garlic to the pan and cook for 5 minutes, or until the meat is browned, stirring all the time. Add the tomato purée, lamb stock, apricots and spinach then season with salt and pepper. Bring to a simmer and cook for 20 minutes, or until the spinach is soft and the liquid has reduced. Set aside.
Take the pasta out of the fridge and divide into four pieces. Roll one piece through a pasta maker on the 0 setting five or six times, then click the machine down a setting and roll through again. Fold the pasta strip, click down another setting and roll through. Continue rolling, folding and clicking down until you reach a setting that produces the thickness of lasagne.
Cut the strip in half and place it on a lightly floured tray. Cover in a clean, damp tea towel while you repeat the rolling with the remaining lumps of dough. You should have eight wide lasagne strips by the time you have finished. You can also make by hand by dividing the pasta dough into eight pieces and rolling very thinly with a rolling pin, keeping around 9cm/3½in wide and roughly 28cm/11in long. Trim the ends before using.
To make the béchamel sauce, melt the butter in a medium saucepan over a low heat and stir in the flour until well combined. Gradually add the milk, stirring with a wooden spoon between each addition. Once all the milk has been added, simmer the sauce very gently for 3 minutes, or until it is smooth and thickened. Season with a little nutmeg, salt and pepper.
Preheat the oven to 180C/Fan 160C/Gas 4. To assemble the lasagne, grease a 2-litre/3½-pint lasagne dish with a little oil. Spoon a third of the meat sauce over the bottom of the dish. Cover with lasagne strips and top with a third of the béchamel sauce. Repeat the layers twice more, ending with the béchamel sauce. Cut the pasta strips to fit the dish as required. (You may not need all of them.)
Crumble the feta over the top and sprinkle with Parmesan. Bake for 30 minutes, or until golden brown and bubbling. Serve.