Preheat the oven to 350°F (175°C). Grease the baking pan or line it with parchment paper.
In a mixing bowl, combine the flour, baking powder, baking soda, salt, and cinnamon. Stir to mix well.
In another bowl, whisk together the vegetable oil, granulated sugar, eggs, and 1 teaspoon of vanilla extract until smooth.
Gradually add the dry ingredient mixture to the wet ingredients, stirring until just combined. Do not overmix.
Fold in the grated zucchini and chopped nuts if using. Mix gently until evenly distributed.
Pour the batter into the prepared baking pan and spread it evenly.
Bake in the preheated oven for 30-40 minutes, or until a toothpick inserted into the center comes out clean.
While the cake is baking, prepare the cream cheese frosting. In a mixing bowl, beat the softened cream cheese until smooth. Gradually add the powdered sugar and the additional teaspoon of vanilla extract, mixing until well combined and creamy.
Once the cake is done baking, remove it from the oven and allow it to cool in the pan for about 10 minutes. Then transfer the cake to a cooling rack to cool completely.
Once cooled, spread the cream cheese frosting evenly over the top of the cake. Slice into squares and serve.