Preheat oven to 350 degrees F (175 degrees C). Grease and flour a muffin pan, or use paper liners.
In a large bowl, combine flour and sugar. Stir in baking powder, baking soda, cinnamon, nutmeg and salt. Cut in shortening until mixture resembles coarse crumbs. Make a well in the center, and pour in milk, eggs, zucchini and vanilla. Fold in walnuts. Fill muffin cups 2/3 to 3/4 full. Sprinkle tops with brown sugar.
Bake in the preheated oven for 15 to 20 minutes, or until a toothpick inserted into the center comes out clean. Allow to cool.