Step 1

Place a rack in middle of oven; preheat to 325°. Lightly coat sides of a 13x9" metal baking pan with nonstick vegetable oil spray. Line bottom of pan with parchment paper. Toast 1½ cups (120 g) pecans on a small rimmed baking sheet until fragrant and deep brown, 12–18 minutes. Let cool; coarsely chop. Increase oven temperature to 375°.

Step 2

Vigorously whisk 2 cups (250 g) bleached all-purpose flour and 2 tsp. baking powder in a large bowl to combine.

Step 3

Blend 3 small carrots (10.5 oz.), scrubbed, trimmed, cut into 1" pieces, 3 large eggs, room temperature, 2 cups (packed; 400 g) light brown sugar, 1 cup vegetable oil, 1 Tbsp. ground cinnamon, 2 tsp. Diamond Crystal or 1¼ tsp. Morton kosher salt, and 2 tsp. vanilla bean paste or vanilla extract in a blender until very smooth, about 2 minutes. Add carrot mixture to bowl with dry ingredients and whisk until just combined (some streaks of dry flour should still be visible). Using a rubber spatula, fold in pecans, 1 cup (140 g) finely chopped dried pineapple rings and ¼ cup (45 g) finely chopped crystallized ginger, scraping down sides and bottom of bowl as needed, until well combined. Scrape batter into prepared pan and jiggle to level surface.

Step 4

Bake cake until golden brown and top springs back when lightly pressed (an instant-read thermometer inserted into the center should register 200°), 25–30 minutes. Transfer pan to a wire rack and let cake cool, about 1 hour. If you prefer to serve the cake unmolded, invert cake onto rack and peel away parchment, then invert cake, right side up, onto a platter.

Step 5

Using an electric mixer on medium speed, beat 8 oz. cream cheese, room temperature, 2 tsp. vanilla bean paste or vanilla extract, and 1 tsp. Diamond Crystal or ½ tsp. Morton kosher salt in a medium bowl until smooth, about 3 minutes. Add 2 cups chilled heavy cream and ⅓ cup (67 g) granulated sugar; beat until frosting holds firm peaks, about 5 minutes. Scrape down sides and bottom of bowl; fold gently to ensure mixture is well combined.

Step 6

Spread frosting over top of cake all the way to the edges with an offset spatula. Using a spoon or offset spatula, create decorative swooshes and swirls in frosting if desired. Dust lightly with ground cinnamon.Do ahead: Cake can be assembled 1 day ahead. Cover and chill. Bring to room temperature before serving.