In a small bowl, cream butter and brown sugar until light and fluffy. Gradually add flour, oats, walnuts and cinnamon until well blended. Press into the bottom and a little up the sides of a greased 9 inch springform pan. Place on baking sheet at 325 for 10 minutes or until set, cool.
In a large bowl, beat cream cheese until fluffy, beat in milk and juice until smooth, add eggs; beat on low speed until combined (batter is thin). Pour into crust.
Return pan to baking sheet, bake at 325 for 45 minutes or until center is almost set. Cool on rack for for 1 hour and refrigerate after that.
In a large skillet, cook and stir gently the apples in butter over medium heat about 5 minutes. Cool. Arrange over cheesecake. In a small saucepan combine cornstarch, cinnamon and juice until smooth. Bring to a boil. Reduce heat and cook and stir for 1 minute or until thickened. Bruch over the apples. Chill. Before serving Garnich with Caramel Ice Cream Sauce, if desired. If not leave plain.