For the Cream Cheese Layer

1. Put the cream cheese that is at room temperature into a mixing bowl. Use an electric mixer to beat it for one to two minutes until it is smooth.
2. Add the egg yolk, sugar, and vanilla extract. Continue beating until everything is fully combined.
3. Place the bowl containing the cream cheese mixture into the freezer. Leave it there while you prepare the remaining parts of the recipe. Chilling the filling helps prevent it from melting completely into the muffins as they bake.

For the Muffins

1. Use a box grater or a cheese grater to grate your carrots. Measure out exactly two cups of grated carrots.
2. In a mixing bowl, combine the all purpose flour, granulated sugar, brown sugar, baking powder, salt, cinnamon, ginger, nutmeg, and cloves. Stir these dry ingredients together with a spoon until they are well mixed. Set this bowl aside for now.
3. In a larger separate mixing bowl, whisk together the eggs, buttermilk, vegetable oil, and vanilla extract. Stir these wet ingredients with a spatula to combine or beat them with an electric mixer on a low speed setting for about 30 seconds.
4. Gradually add the dry ingredients from the first bowl into the wet ingredients. Mix the batter only until the dry ingredients are just combined with the wet. Do not overmix.
5. Use a spatula to gently fold in the grated carrots. The muffin batter will be quite thick at this stage.
6. Cover the bowl of batter with a clean towel. Let the batter sit and rest for 15 minutes. While the batter rests, preheat your oven to 425 degrees Fahrenheit (220 degrees Celsius).

Assemble

1. After the 15 minute resting period is finished, line a muffin tin with paper liners. Fill each muffin cup with only one to two tablespoons of the prepared muffin batter.
2. Next, add one to two tablespoons of the cold cream cheese mixture on top of the small amount of batter in each cup.
3. Finally, top each muffin cup with more muffin batter. Fill the cups all the way to the very top. It is important to start with just a small amount of batter before adding the cream cheese filling. If the cream cheese filling is placed too high in the cup, it might ooze out the top while baking.
4. Optionally, you can sprinkle the tops of the filled muffin cups with sanding sugar for a sparkling finish.
5. Place the muffin tin in the preheated 425 degrees Fahrenheit (220 degrees Celsius) oven and bake for 7 minutes. Do not remove the muffins from the oven.
6. After the initial 7 minutes, turn the oven temperature down to 350 degrees Fahrenheit (175 degrees Celsius). Continue baking for another 12 to 15 minutes. You will know they are done when a toothpick inserted into the center of a muffin comes out clean.
7. Let the baked muffins cool inside the muffin pan for at least 15 minutes before you attempt to remove them. Sometimes the cream cheese filling may create a slightly hollow space inside the muffin as it melts. Freezing the cream cheese filling ahead of time can help minimize this effect.
8. If you have more batter, repeat the baking process with a second batch. Remember to raise the oven temperature back up to 425 degrees Fahrenheit (220 degrees Celsius) again for the first 7 minutes before lowering it to 350 degrees Fahrenheit (175 degrees Celsius).