Prepare the zucchini. Grate with a box grater then place in a tea towel or muslin cloth and squeeze as much water out as you can. After squeezing I had 440 grams of grated zucchini. A bit more or less is fine!
Heat the olive oil in a large skillet that will fit all the pasta on a medium heat and add the zucchini, onion and garlic.
Lower the heat, add a couple of big pinches of salt and gently cook down for 20 - 25 minutes until pretty much all of the moisture is gone and it is thick and jammy. Adjust your heat as needed, a low heat will be best.
Stir every couple of minutes and you know it is ready when it is sticking to the bottom of the pan. See video below or photos above for reference.
Remove the mixture from the pan and set aside in a bowl.
While zucchini is cooking, cook your pasta, reserving a cup of the pasta water before draining.
Add the cream to the empty pan the zucchini was in and bring to a very gentle simmer, it should never boil at any point so keep your heat low.
Add the finely grated parmesan in 2 - 3 separate lots, letting it melt in between each addition.
Add the black pepper and lemon juice and and mix in quickly.
Add ¼ cup of pasta water and mix. Let it gently simmer for a minute or two to thicken slightly.
Add the zucchini mixture to the cream and mix in well then add your cooked pasta and toss well.
Season with salt to taste.
Let it very gently bubble away for a min or two and add another ¼ cup pasta water to loosen if needed.
Toss the basil leaves through right before serving and serve with lemon zest and extra parmesan on top.