Preheat the oven to 350°F (175°C). Grease and flour the 9x9 inch baking pan or line it with parchment paper.
In a large mixing bowl, combine the flour, sugar, baking powder, baking soda, ground cinnamon, and salt. Whisk together until well mixed.
In a separate bowl, beat the egg, then add the vegetable oil and vanilla extract. Mix until combined.
Add the wet ingredients to the dry mixture and stir until just combined. Be careful not to overmix; a few lumps are okay.
Fold in the grated zucchini and the optional chopped nuts, if using.
Pour the batter into the prepared baking pan and spread it evenly.
In a small bowl, combine the brown sugar and the additional ground cinnamon. Sprinkle this mixture evenly over the top of the batter.
Bake in the preheated oven for 30 minutes, or until a toothpick inserted in the center comes out clean.
Allow the coffee cake to cool in the pan for a few minutes before transferring it to a wire rack to cool completely.