In a large pot bring water to a boil on high heat adding a generous amount of salt. Add the pasta, stirring occasionally so as not to stick and cook according to suggested time on the box of the pasta less 1½’. Reserve 1 cup of cooking water.
In the meantime, in a large and deep pan over medium heat pour the olive oil and toss in onions. Sauté for 3’ and add the garlic. A minute later add the sliced zucchinis, coriander and chilli flakes and fry for about 5-7’ until softened and a bit charred. Discard the garlic, season with the salt and pepper and remove from the heat. Keep aside in the pan.
While frying the zucchinis, take a medium bowl and lightly beat the eggs along with grated cheeses to create a smooth cream.
Strain the pasta and return to the saucepan with the zucchinis, which is set on very low fire and cook for another a minute. Remove from fire, add ½ cup of the reserved pasta water and toss to cool a bit, while stirring add the eggs/cheese mixture, stirring for further 30’’ so as the pasta absorbs the sauce. Add more from the reserved water if required.
Serve in a deep dish, add some more grated cheeses and a crack of freshly cracked black pepper.