Begin by preheating your oven to 350°F and preparing a 12-cup muffin tin by lining it with paper liners.
In a large mixing bowl, sift together the dry ingredients: flour, baking soda, salt, ground nutmeg, and ginger, ensuring they are well combined.
In a separate bowl, whisk the wet ingredients: melted butter, honey, applesauce, shredded carrots, beaten egg, and vanilla extract until fully incorporated.
Form a well in the center of the dry ingredients, then gradually pour the wet mixture into it. Gently stir everything together, being careful not to overmix to avoid dense muffins.
Evenly distribute the batter into the muffin tin and bake for approximately 12 minutes. Test for doneness by inserting a clean knife into the center of a muffin—if it comes out clean, they are ready. For optimal texture, remove them from the oven just before full doneness, as they will continue cooking while cooling.
As the muffins cool on a wire rack, prepare the yogurt glaze. Combine the yogurt with powdered sugar, and if desired, add a few drops of food coloring for a decorative touch.
Once the muffins have cooled, drizzle the yogurt glaze over the top. Enjoy these nutritious and flavorful muffins as a delightful treat.