Preheat the oven to 375°F (190°C). Line a 12-cup muffin tin with paper liners or lightly grease the cups.
Place the cottage cheese, eggs, oil, brown sugar, granulated sugar, vanilla and orange zest into a blender or food processor. Pulse until mostly smooth; a few tiny curds are fine. This creates a silky wet base without needing separate creaming.
In a large bowl whisk together the flour, baking powder, baking soda, salt and cinnamon until evenly combined.
Pour the blended wet mixture into the dry ingredients and stir gently with a rubber spatula until just moistened. The batter will be thicker than pancake batter but not dry.
Fold in the grated carrots and chopped walnuts until distributed. Let the batter rest 8–10 minutes at room temperature to hydrate the flour and help lift during baking.
Spoon the batter into the prepared muffin tin, filling each cup about three-quarters full. Top each muffin with a walnut half if desired.
Bake for 16–20 minutes, rotating the pan halfway through, until the tops are golden and a toothpick inserted in the center comes out clean or with a few moist crumbs.
Allow muffins to cool in the pan for 5 minutes, then transfer to a wire rack to cool completely. Store cooled muffins in an airtight container in the fridge for up to 5 days.