1. Preheat your oven to 350 F (175 C). Lightly grease and flour a 9×13-inch baking pan, or line it with parchment paper, leaving an overhang on the sides to easily lift the bars out later. This prevents sticking and makes cleanup a breeze.

2. In a large bowl, whisk together the all-purpose flour, baking soda, salt, ground cinnamon, ground nutmeg, and ground ginger. Make sure there are no lumps and the spices are evenly distributed. This ensures a consistent flavor throughout your bars.

3. In a separate medium bowl, whisk together the granulated sugar, light brown sugar, vegetable oil, eggs, and vanilla extract until well combined and smooth. The sugars should be mostly dissolved.

4. Pour the wet ingredients into the dry ingredients. Mix with a spatula until just combined; be careful not to overmix. Gently fold in the grated carrots and optional chopped pecans or walnuts. The batter will be thick and vibrant with orange carrot flecks.

5. In a small bowl, beat the softened cream cheese with 1/4 cup granulated sugar, the egg yolk, and 1/2 teaspoon vanilla extract until completely smooth and creamy. There should be no lumps of cream cheese.

6. Spread the carrot cake batter evenly into your prepared 9×13-inch baking pan. Dollop spoonfuls of the cheesecake mixture over the carrot cake batter. Use a knife or a skewer to gently swirl the cheesecake into the carrot cake batter, creating attractive patterns. Do not overmix the swirl; you want distinct layers.

7. Bake for 25-30 minutes, or until a toothpick inserted into the carrot cake portion comes out clean. The cheesecake swirl might still look slightly soft, but it will firm up as it cools. The edges of the bars should be lightly golden brown.

8. Let the bars cool completely in the pan on a wire rack before cutting. If desired, whisk together the powdered sugar, milk or orange juice, and 1/4 teaspoon vanilla extract for the glaze. Drizzle the glaze over the cooled bars before slicing and serving.