Preheat oven to 375°F (190°C). Line a 12-cup muffin pan with liners or lightly grease it.
In a medium bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, nutmeg, and ginger.
In a large bowl, whisk together the sugars, melted butter, oil, eggs, buttermilk, and vanilla until smooth.
Gradually add the dry ingredients to the wet ingredients, stirring gently until just combined. Fold in the shredded carrots and pecans.
Divide the batter evenly among the muffin cups. Bake for 18-22 minutes or until a toothpick inserted in the center comes out clean. Let cool in the pan for 5 minutes, then transfer to a wire rack to cool completely.
To make the cream cheese glaze:
Mix together the cream cheese, confectioner's sugar, 2 tablespoons of milk (or cream), and vanilla until smooth. Add more milk (or cream) as needed to get the desired consistency.
Drizzle, dip, or spread over the cooled muffins.
Notes
Store unglazed muffins in an airtight container at room temperature up to 2 days.