Preheat oven to 350°F and line a loaf pan with lightly greased parchment paper.
Combine oats and coconutmilk beverage in a large bowl; let sit 20 minutes
Meanwhile, combine flaxseed meal with 2 Tbsp water; let sit 5 minutes.
Pour flaxseed mixture into bowl with soaked oats. Stir in maple syrup, coconut oil, vanilla, and coconut sugar; whisk to combine. Fold in grated carrots.
In a separate bowl, combine flour, baking powder, cinnamon, ginger, and salt; stir with a whisk.
Combine flour mixture and carrot mixture; stir until just combined (do not overmix). Fold in ½ cup of the chopped walnuts.
Pour batter into prepared loaf pan and scatter remaining ¼ cup chopped walnuts on top. Bake until loaf is golden brown and firm, and a toothpick or knife comes out mostly clean, about 1 hour 15 mins.
Let rest for 10 minutes in pan; remove from pan and let cool completely on a wire rack.
Store leftovers covered at room temperature for up to 4 days, or slice and freeze for up to 1 month. Reheat in the microwave or toaster oven until tender and warmed through.