Apple-Ginger Snack Cake

Ingredients

• Cake:
• 1 cup chopped walnuts
• 2 cups all-purpose flour
• 1 teaspoon baking soda
• 1 teaspoon cinnamon
• 2 teaspoons ground ginger
• 1 teaspoon salt
• 8 tablespoons (1 stick) unsalted butter, melted
• 1 1/2 cups sugar
• 2 large eggs, lightly beaten
• 1 teaspoon vanilla extract
• 4 large Granny Smith apples (about 2 lb.), peeled, cored and chopped
• Frosting:
• 6 ounces cream cheese, at room temperature
• 2 tablespoons unsalted butter, at room temperature
• 2 tablespoons lemon juice
• 1 cup confectioners' sugar, sifted
• 1 teaspoon lemon zest
• 1/4 cup chopped crystallized ginger