Prep and preheat: Heat your oven to 375°F (190°C). Line a 12-cup muffin tin with paper liners.
Make the flax “egg”: Stir the ground flaxseed with water in a small bowl. Let it thicken for about 5 minutes until gel-like.
Whisk dry ingredients: In a large bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, ginger, and nutmeg. Break up any clumps.
Mix wet ingredients: In another bowl, whisk the brown sugar, maple syrup, oil, non-dairy milk, vanilla, and orange zest until smooth. Stir in the flax mixture.
Combine: Pour the wet ingredients into the dry. Stir gently until just combined, a few small streaks of flour are fine. Do not overmix.
Fold in carrots and add-ins: Add the grated carrots along with any optional add-ins like walnuts, raisins, coconut, crushed pineapple, or chopped dates. Fold gently until just combined.
Portion the batter: Divide evenly among the muffin cups, filling each about 3/4 full for a nicely domed top.
Bake: Bake for 18 to 22 minutes, until the tops are set and a toothpick inserted into the center comes out with a few moist crumbs.
Cool: Let the muffins rest in the pan for 5 minutes, then transfer to a wire rack to cool completely.
Glaze and garnish: Whisk the powdered sugar with fresh orange juice until thick but pourable. Drizzle over fully cooled muffins. While the glaze is still slightly wet, sprinkle with chopped pistachios, toasted coconut, or finely chopped candied orange peel so everything sets in place beautifully.