Use a box grater or food processor to coarsely grate the zucchini. If using zucchini blossoms, roughly chop them.
In a wide, deep sauté pan or sauce pan over low heat, warm 3 tablespoons olive oil. Add the onion along with a good pinch of salt and cook, stirring occasionally, until softened and translucent, 7 to 10 minutes.
Add the rice to the pan and stir until the grains of rice are glistening and thoroughly coated, about 2 minutes. Pour in the white wine and bring the heat up to medium. Let the wine simmer until almost completely absorbed, about 5 minutes. Then add just enough warm vegetable broth to cover the rice, about 1 ladleful or 3/4 cup. Continue to cook, stirring occasionally and adding a ladleful of broth at a time as the liquid reduces (about every 5 minutes). After 10 to 15 minutes, add the grated zucchini. Continue to cook, stirring occasionally, and topping up with broth as needed for another 7 to 10 minutes, or until the rice is al dente. You'll need to add a total of 4 1/2 to 6 cups broth to the risotto, depending on just how creamy you wish your risotto to be. With the last addition of broth, add the grated cheese, if using, and salt to taste. Add 1 tablespoon oil and stir until the risotto becomes creamy but still sorta soupy or, as the Italians say, loose. (Don’t worry. The risotto will become slightly thicker and stiffer as soon as it begins to cool on the plate.)
Remove the risotto from the heat. If using the zucchini blossoms, toss them in the pan and gently stir just until they wilt. Remove from the heat and immediately ladle the risotto immediately onto warm rimmed plates. Sprinkle with freshly ground black pepper and, if desired, a little extra grated cheese. Serve right away. In fact, everyone should be seated at the table and waiting by the time you’re ladling risotto onto plates.