Preheat the oven to 400 degrees. Use a 18 count muffin pan if you have, or a 12 count and a 6 count muffin and spray them with non-stick baking spray.
Beet the oil, sugars and orange extract until well combined. Add the eggs and beat again.
In a separate bowl, mix the flour, baking powder, baking soda, cinnamon, nutmeg, and salt. Add the dry ingredients into the wet slowly, while string together.
Add the buttermilk and carrots and stir again until everything is combined.
Spoon the batter in each muffin tin evenly.
To make the cheesecake filing, mix together the cream cheese, sugar, orange extract, and flour. Spoon the mixture into 2 large plastic bags and cut the tip of each bag.
Squeeze half of the cheesecake filing into the center of each muffin. With the second bag, make a swirl of cheesecake at the top of each muffin.
Sprinkle the pecans on top.
Bake for 15-16 minutes.