Apple Crumb Cookies

Name: Apple Crumb Cookies
Cuisine: American
Ingredients: 3 large apples peeled and small diced ((cut them into pea size) I used granny smith); 1 tablespoons lemon juice; 1/2 cup granulated sugar; 3/4 teaspoon ground cinnamon; pinch of salt; 2 tablespoons corn starch; 1/4 cup cold water; ½ cup dark brown sugar; 3/4 cup all purpose flour; 1 teaspoon ground cinnamon; Pinch of salt; 4 tablespoons unsalted Butter room temperature; 1 cup unsalted Butter; 1/2 cup light brown sugar; 1/2 cup granulated Sugar; 1 large egg; 1 large egg yolk; 2 teaspoons Vanilla extract; 2 2/3 cup all purpose flour; 1 teaspoon cornstarch; 1 ½ teaspoon baking powder; ½ teaspoon salt; 2 teaspoon cinnamon; 3/4 cup powder sugar; 2 tablespoons milk or water