To a small mixing bowl, add the softened cream cheese, granulated sugar, and vanilla extract. Use a small spoon or rubber spatula to combine the ingredients until the mixture is smooth. Be sure that your cream cheese is very soft in order to get a nice smooth texture to the filling.

Using a very small cookie scoop or small spoon, scoop out 12 (approximately 2 teaspoon-sized) dollops and place them onto a small, parchment-lined, freezer-safe cookie sheet or baking pan. Lightly cover with plastic wrap and freeze the cream cheese dollops for at least 2 hours (or up to overnight) or until frozen solid.

Preheat oven to 350°F. Line 2 large cookie sheets with parchment paper and set aside.

In a small bowl, stir together the all-purpose flour, ground cinnamon, baking soda, salt, and ground nutmeg. Set aside.

To a large mixing bowl add the room temperature unsalted butter, light brown sugar, and granulated sugar. Beat on medium speed using a handheld mixer for 1-2 minutes or until light and fluffy.

To the beaten butter, add the large egg and vanilla extract. Beat again for 30 seconds to 1 minute until the mixture is smooth and the egg is fully incorporated. Add the shredded carrots and mix on low just until the shredded carrots are fully incorporated.

Add the flour mixture to the bowl of wet ingredients and mix on low speed just until all the flour has been incorporated, the dough comes together, and it's no longer crumbly. The dough will be very thick and just slightly sticky to the touch.

Using a 2-inch or 2-tablespoon cookie scoop, scoop out a leveled scoop of dough. Using your finger, carefully create a well in the center of the dough while it's still in the cookie scoop. You will now have dough that lifts taller than the edge of the scoop. This will make it easier to stuff and shape the slightly sticky cookie dough.

Place one of the frozen cream cheese dollops into the well of the carrot cake cookie dough, then gently cover the cream cheese with the sides of the dough that has been pushed up on the sides of the cookie scoop.

Squeeze the cookie scoop handle to release the dough ball into the palm of your hand, and gently roll the dough to create a smooth ball. Place the ball onto one of the prepared baking sheets. Repeat until all the cookies have been filled and shaped and placed onto the prepared baking sheets. You should be able to fit 6 cookie dough balls, spaced about 2-3 inches apart, onto each of the prepared baking sheets.

Bake the cookies (with the baking sheets evenly spaced) in the center of the preheated oven for 13-15 minutes or until lightly golden around the edges.

Allow the baked cookies to cool on the baking sheet on the counter for at least 15 minutes before transferring them to a wire rack to cool completely. This allows the cream cheese filling to set up and firm before serving.