1. Preheat oven to 350 degrees Fahrenheit. Line cups of a standard (12-cup) muffin tin with paper or foil liners. Set aside.
2. In a medium bowl, mix together flour, brown sugar, baking powder, cinnamon, and salt. Mix in nuts. In another bowl, combine zucchini, oil, eggs, and vanilla; add to flour mixture, and mix just until combined (do not overmix).
3. Divide batter evenly among cups. Bake until a toothpick inserted in the center of a cupcake comes out clean, 40 to 45 minutes.