Preheat the oven to 375°F (190°C). Line a muffin tin with paper liners or grease it well.
In a bowl, whisk together flour, baking powder, baking soda, salt, cinnamon, and any optional spices.
In a second bowl, whisk brown sugar, granulated sugar, eggs, oil, applesauce (if using), and vanilla until smooth.
Fold the dry ingredients into the wet ingredients just until combined—stop as soon as you don’t see dry flour.
Fold in the grated carrots and any add-ins (nuts/raisins).
Divide batter evenly into the muffin cups, filling each about ¾ full.
Bake for 18–22 minutes, or until the tops spring back lightly and a toothpick comes out clean (a few moist crumbs are fine).
Cool in the pan for 5 minutes, then transfer muffins to a rack to cool completely.
If adding cream cheese glaze, beat cream cheese until smooth, mix in powdered sugar and vanilla, then thin with a splash of milk or lemon juice until drizzle-able. Spoon or drizzle over cooled muffins.