Preheat your oven to 350°F (180°C) and line a muffin pan with paper liners or lightly grease silicone muffin cups.
In a large bowl, whisk together the oil, brown sugar, egg, vanilla, baking powder, baking soda, cinnamon, ginger, nutmeg, cloves, and salt until smooth.
Stir in the flour until just combined, then fold in the grated carrots and chopped nuts if using.
Divide the batter evenly into the muffin cups, filling each about two-thirds full.
Bake for 22 to 25 minutes, or until a toothpick inserted into the center comes out clean.
Let the muffins cool in the pan briefly, then transfer them to a wire rack to cool completely.
For an optional cream cheese topping, beat the cream cheese with the honey and vanilla until smooth, then spoon over cooled muffins.
For an optional glaze, whisk together the powdered sugar, vanilla, milk or water, and a pinch of salt until pourable, then drizzle over the muffins.
