Danish Creamery : Apple Cardamom Cake

Ingredients

• ⅔ cup all-purpose flour
• ½ cup granulated sugar
• ¼ teaspoon fine salt
• ½ cup finely chopped, toasted walnuts
• 4 Tablespoons Danish Unsalted Butter, melted
• 2 Tablespoons Danish Unsalted Butter
• ¼ cup granulated sugar
• pinch of cinnamon
• 2 cups peeled and finely diced Granny Smith apples (about 3 medium apples)
• 2 ½ cups all-purpose flour
• ¾ teaspoon baking powder
• ¼ teaspoon baking soda
• ½ teaspoon Kosher salt
• 1 teaspoon ground cardamom
• ¼ teaspoon ground cinnamon
• 10 Tablespoons Danish Unsalted Butter, room temperature
• 1 ¼ cups granulated sugar
• 2 large eggs plus 1 egg yolk, room temperature
• 1 ½ teaspoon vanilla extract
• 1 cup buttermilk, room temperature
• 2 ounces cream cheese, softened
• 1 Tablespoon Danish Unsalted Butter, softened
• ½ cup powdered sugar
• ½ teaspoon vanilla extract
• 2 Tablespoons heavy cream, plus more if needed for a glaze consistency