Apple Spice Cookies with Brown Butter Icing

Ingredients

• 1 tablespoon butter
• 1 cup (4 oz or 113g) chopped apples (1/4-inch pieces) (I used one large Granny Smith apple)
• 1 tablespoon sugar
• 1/4 teaspoon ground cinnamon
• 1 1/2 cups (6 3/4 oz or 191g) all purpose flour, sifted
• 1/2 teaspoon baking soda
• 1/2 teaspoon salt
• 1 teaspoon ground cinnamon
• 1/4 teaspoon ground nutmeg
• 1/2 cup (4 oz 113g) unsalted butter, softened
• 1 cup (7 oz or 200g) packed brown sugar
• 1 large egg
• 1 large egg yolk
• 1/2 teaspooon pure vanilla extract
• 2 tablespoons unsalted butter
• 1/2 cup (2 oz or 57g) powdered sugar, sifted
• 1/2 teaspoon pure vanilla extract
• pinch fine sea salt
• 1-2 tablespoons whole milk