Step 1

Place 1 stick unsalted butter for the cake in the bowl of a stand mixer and let sit at room temperature until softened.

Step 2

Arrange a rack in the middle of the oven and heat the oven to 300°F. Meanwhile, line a 9-inch square baking pan with a parchment paper sling that has a 2-inch overhang over two sides. Coat the pan and paper with cooking spray. Peel and grate 1 to 2 medium carrots on the large holes of a box grater until you have 1 lightly packed cup. Drain 1 can crushed pineapple through a fine-mesh strainer set over a bowl. Reserve the juice.

Step 3

If using walnuts, spread 1/2 cup on a rimmed baking sheet. Bake until fragrant and toasted, 8 to 10 minutes. Set aside to cool. Meanwhile, make the topping.

Step 4

Cut 1 stick unsalted butter into 1/2-inch cubes and place in a medium bowl. Add 1/2 cup granulated sugar, 3/4 cup all-purpose flour, and 1 teaspoon ground cinnamon. Rub the butter into the mixture with your fingers until it clumps together when you squeeze it in your hand. Don’t over work it as you want to have a crumb with both large and small crumbles. Refrigerate while you make the cake.

Step 5

Increase the oven temperature to 350°F. Place 2 1/2 cups all-purpose flour, 2 teaspoons ground cinnamon, 1 teaspoon baking powder, 1/2 teaspoon baking soda, and 1/2 teaspoon kosher salt in a medium bowl and whisk to combine.

Step 6

Add 1 cup granulated sugar to the butter in the stand mixer bowl. Beat with the paddle attachment on medium speed until pale and fluffy, scraping down the bowl about halfway through, about 4 minutes total. Beat in 2 large eggs one at a time and until fully incorporated. Add 1 cup sour cream and 2 teaspoons vanilla extract, and beat to combine.

Step 7

If using walnuts, coarsely chop. Add the walnuts, pineapple, and carrots to the batter and mix on low speed until just combined. Beat the flour mixture mix in on low speed just until incorporated - do not overmix. Transfer to the prepared baking pan and spread into an even layer. Sprinkle evenly with the topping.

Step 8

Bake until the top is golden brown and a toothpick inserted into the center comes out with just a few crumbs clinging to it, 40 to 45 minutes. Meanwhile, place 4 ounces cream cheese in a medium bowl and let sit at room temperature to soften.

Step 9

Let the cake cool in the pan for 15 minutes. Grasping the excess parchment paper, lift the cake out of the pan and place on a wire rack to cool completely. Meanwhile, make the drizzle.

Step 10

Add 1/2 cup powdered sugar and 3 tablespoons of the reserved pineapple juice to the cream cheese and whisk until combined and smooth. Add more pineapple juice a teaspoon at a time as needed until it drizzles off the whisk in ribbons. Drizzle onto the cooled cake before serving.