Preheat oven to 350º F / 180º F. Grease or line a 12 cup muffin pan.
In a large bowl, whisk together the first seven ingredients. In a separate large bowl, whisk together oil, eggs, and vanilla and mix well, whisk in brown sugar and mix until smooth. Add zucchini, stirring to incorporate; add flour mixture and stir until just combined. Stir in cheese.
Spoon batter into the muffin pan, filling each one three-quarters full. Bake for 20 minutes or until a cake tester inserted in the middle comes out clean. Rotate halfway through the baking process to promote even baking.
Transfer to a wire rack; let cool completely before turning out. Serve.