Spring Celebration Carrot Cake

INGREDIENTS

• 1 1/2 cups sugar
• 2 (4-ounce) jars pureed carrot baby food
• 12 tablespoons (1 1/2 sticks) unsalted butter, cubed, at room temperature
• 1/2 teaspoon freshly grated nutmeg
• 4 large eggs
• 1 1/4 cups vegetable oil
• 2 1/4 cups all-purpose flour
• 1/2 cup finely chopped fresh pineapple (see Cooks Note)
• 1 1/2 tablespoons finely grated lemon zest (about 2 lemons)
• 1 cup walnut pieces
• 2 teaspoons ground cinnamon
• 1 teaspoon baking soda
• 1 1/2 cups fresh pineapple
• 1 1/2 cups grated fresh carrots (about 2 large)
• 1 teaspoon pure vanilla extract
• 1/2 teaspoon ground ginger
• 1 teaspoon baking powder
• 2 cups confectioners' sugar
• 2 (8-ounce) packages cream cheese (1 pound), at room temperature
• 1/2 teaspoon fine salt