Position a rack in the middle of the oven and preheat to 350°F. Lightly coat the cups of 2, 12-cup muffin tins with shortening.
Sift together twice onto a piece of waxed paper, the flour, baking powder, baking soda, salt and nutmeg.
In a large bowl, whisk the eggs. Whisk in the granulated and brown sugars and then the oil, lemon zest and vanilla extract. Stir in the zucchini. Stir in the flour mixture until almost combined. Add the walnuts and stir just until combined. Divide the batter between the prepared tins, filling each cup no more than three-quarters full.
Bake until the muffins are puffed and just beginning to pull away from the sides of the cups and a tester, inserted into the middle of a muffin, comes out clean, 20-25 minutes.
Remove the pans from the oven and let the muffins stand in the tins on a rack for 10 minutes. Turn out and serve warm or at room temperature.Note: The muffins can be made with 2 cups grated unpeeled raw apple in place of the zucchini.Makes 24