Preheat your oven to 375°F (190°C). Line a 12-cup muffin tin with paper liners or grease the cups lightly.
In a large bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, and nutmeg until well combined.
In a separate bowl or large measuring jug, whisk the eggs, oil, granulated sugar, brown sugar, vanilla, and yogurt until smooth and slightly thickened.
Make a well in the dry ingredients and pour in the wet mixture. Stir gently with a spatula until the batter is mostly combined. Do not overmix; a few small streaks of flour are fine.
Fold in the grated carrots and walnuts (and any optional add-ins) just until evenly distributed.
Divide the batter evenly among the muffin cups. For a taller dome, fill each cup about three-quarters full. Sprinkle the tops with coarse sugar if using.
Bake for 18–22 minutes, or until the tops are set and a toothpick inserted in the center comes out clean or with a few moist crumbs.
Cool in the pan for 5 minutes, then transfer the muffins to a wire rack to cool completely or enjoy slightly warm.