Preheat oven to 350 degrees. Grease a 9-inch cake pan with coconut oil and line the bottom with a round of parchment paper.

Drain one 20-ounce can crushed pineapple in a strainer over a bowl. Press on the solids to expel as much liquid as possible. You should have about 1 cup (8 ounces) of lightly packed pineapple. Discard the liquid or reserve for another use.

Peel and chop 8 ounces carrots into 2-inch pieces. Add to a food processor and process until finely chopped. Add ½ cup buttermilk, 2 eggs, 1 ½ cups sugar, 1 tablespoon vanilla, and ½ cup melted coconut oil. Blend until combined, 3-5 seconds.

Add 1 ½ cups flour, 1 ½ teaspoons baking soda, 1 ½ teaspoons cinnamon, and ¾ teaspoon kosher salt. Blend until just combined and no traces of flour remain, scraping down the bowl once, 4-6 seconds.

Add the drained pineapple and 4 ounces walnuts. Pulse to combine, keeping the walnuts large.

Scrape into the prepared cake pan and transfer to the oven. Bake until a toothpick comes out clean, about 36-44 minutes.

For the soak, combine the remaining 1 cup + 2 tablespoons sugar, the remaining ⅔ cup buttermilk, the remaining 2 teaspoons vanilla, and 1 teaspoon salt in a small saucepan. Bring to a boil and cook, whisking, until bubbling ferociously. Cook 2 minutes. Remove from heat and add the remaining ¼ cup coconut oil.

Transfer ½ cup of the buttermilk soak to a large bowl. Let cool until warm, or transfer to the fridge to speed up the process. Add one (12-ounce) container Philadelphia cream cheese spread and ¼ teaspoon salt to the large bowl. Whisk until smooth. The consistency should be thick but spreadable. If necessary, use buttermilk - a teaspoon at a time - to thin to a spreadable consistency. Keep at room temperature until ready to frost.

When the cake comes out of the oven, immediately poke holes all over the top with a toothpick. Pour the remaining buttermilk soak all over the hot cake, letting it seep in. Cool the cake until warm. Run a knife around the edges of the pan and invert onto a cake stand. Let cool completely.

Frost the cake as desired. Cut into wedges and serve.