Preheat the oven to 350°. Generously butter a 9" springform pan, 9" x 2" round pan, or three 6" round pans. Dust the pan/s with flour and tap out any excess.
Grate the zucchini, lemon zest, and ginger and set aside.
Combine the flour baking powder, baking soda, ground ginger, and salt in a medium bowl and whisk together well. Set aside.
In a stand mixer with paddle attachement or with a handheld mixer, beat together the sugar and eggs until creamy and slightly fluffy, about 2-3 minutes. Scrape down the sides of the bowl.
Again turn the mixer to medium speed and add the olive oil in a steady stream. Continue mixing in the olive oil until fully incorporated and quite fluffy, another 3 minutes. Again scrape down the sides of the bowl.
With the mixer at low speed, quickly add the flour mixture one cup at a time, not waiting for it to fully incorporate. Turn the mixer off and remove the mixing bowl.
Add the grated zucchini, lemon zest, and ginger to the bowl, and gently stir with a rubber or silicone spatula, folding up from the bottom, until the grated ingredients are evenly mixed through the batter.
Pour the batter into the prepared cakepan/s and smooth the top and bake. For the 9" pans, bake for 50-60 minutes until the top springs bake when gently pushed and the edges are just beginning to pull away from the pan, and a bamboo skewer or toothpick inserted in the center comes out clean. for the 6" pans, bake 35-45 minutes. It is easy to underbake this cake, especially the larger pans, so take extra care to make sure they are done in the center.
Allow the cake to cool 15 minutes before inverting on a cooling rack. While the cake is cooling, make the glaze.