In a saucepan, warm up the vegetable broth or stock, and keep it warm throughout the cooking process.
Grate the zucchini using the large holes of a grater, and set aside.
Finely chop an onion.
Add the extra virgin olive oil to a heavy-bottomed sauce pan or Dutch oven and heat up on low to medium heat. Once warm, add the thinly chopped onion and a sprinkle of salt, and mix well.
Allow the onion to cook for 5 minutes until transparent and soft. Don't allow the onion to brown. Reduce the flame to low if necessary.
Increase the heat to medium high, and add the risotto rice and toast is until its edges start turning translucent and the rice looks lighter in color. This will take about a minute.
OPTIONAL: At this stage, add the white wine if you decide to use it. Mix the rice well and allow the alcohol to be completely evaporated before proceeding to the next step.
Reduce the heat to low once again, and add a couple of ladels of vegetable stock or broth to the risotto, and mix.
Keep on adding broth as required, and mix well every couple of minutes, to allow the rice to release its starch. Keep the flame on low, allowing the risotto and broth to lightly simmer, but not boil.
Once the rice is halfway cooked [about 9-10 minutes], add the grated zucchini and mix well.
Allow to cook like this for a further couple of minutes, then return to adding broth and mixing.
Once the zucchini risotto is cooked, remove it from the heat. Add the butter, grated Parmesan cheese, lemon zest, and white pepper.
Mix well and allow the risotto to rest for a couple of minutes before serving.
If you'd like to garnish it, I suggest frying in a little olive oil some thin zucchini roundels until golden!