Preheat oven to 350F and grease an 8" x 8" pan with nonstick spray.
In a medium bowl with a spatula or wooden spoon, stir together the eggs, carrots, oil, applesauce, and honey.
Add the flour, cinnamon, baking powder, baking soda, and raisins to the bowl with the egg mixture and gently fold together, taking care not to overwork the flour.
Pour mixture into prepared pan and use a spatula to spread the batter evenly in the pan.
Bake for 24-28 minutes, or until golden brown around the edges and a cake tester inserted into the center comes out clean. Let cool for about 10 minutes, then carefully invert onto a wire rack to cool fully.
Frost if desired. (See Notes for the frosting recipe.)
To make the Cream Cheese Frosting: In a large bowl with a handheld electric mixer, beat 6 ounces cream cheese, softened to room temperature, 1 teaspoon vanilla extract, and 1/4 cup honey honey for 30 seconds, stopping to scrape down the sides of the bowl as needed. Spread frosting over the cooled cake, then carefully cut into 12 bars and serve.
Bars can be made up to 24 hours ahead. Store in an airtight container at room temperature and frost before serving. Leftovers can be stored in the fridge for up to 3 days in an airtight container.
Gluten-free: Use 1:1 style of gluten-free flour blend.