Preheat the oven to 375 degrees F. Coat an 8x8-inch baking pan (metal is best) with nonstick spray. (I also line with parchment paper so it's easy to lift out and slice without scratching the pan. That is optional.)
In a large bowl, stir together the carrots, applesauce, eggs, butter, and vanilla.
Add the flour, brown sugar, cinnamon baking powder, baking soda, and salt.
Gently stir the carrot mixture into the flour mixture. Stir in the raisins.
Pour batter into the prepared pan, smoothing out the top.
Bake for 22-24 minutes, or until the edges are lightly golden brown and a cake tester inserted into the center comes out cleanly.
Let cool and top with Cream Cheese Frosting, if desired.
Notes
Once cooled, store in an airtight container for up to 3 days at room temperature. Store in the fridge in an airtight container for up to 5 days. Serve cold.
You can also freeze the cut cake, frosted or unfrosted (though unfrosted is cleaner) in a freezer bag with as much air removed as possible for up to 3 months. Thaw at room temperature or in 15 second increments in the microwave.
This bakes best in a metal pan, rather than glass. If baking in glass, the middle will take longer to set. Follow the recipe, then cover with foil and bake for an additional 10 minutes.
Gluten-free: Substitute cup-for-cup gluten-free flour in place of the wheat flours.
Top with Cream Cheese Frosting. Soften 8 ounces cream cheese and 1/4 cup unsalted butter at room temperature. Add to a bowl with 1/4 cup honey (for kids over age 1) and 1 teaspoon vanilla. Start mixing on low with a handheld mixer until fluffy. Place on top of the cooled bars and spread evenly.
Dairy-free: Use oil in the batter and vegan cream cheese and butter in the frosting.
If you prefer your baked goods sweeter (or if you leave out the raisins) increase the brown sugar to 1/2 cup.