How to Make It
Preheat oven to 350°F with oven rack in lower third of oven. Wrap bottom and sides of a 7-inch springform pan tightly with aluminum foil. (This will prevent any moisture getting into cheesecake.) Trim any excess foil from around the top of the pan.
Prepare the Crust: Stir together crumbs, granulated sugar, cinnamon, and melted butter in a medium bowl until well combined. Press into bottom and 1 1/2-inches up sides of prepared springform pan. Bake in preheated oven until golden brown, about 10 minutes. Transfer to a wire rack, and cool completely, about 20 minutes.
Prepare the Filling: Beat cream cheese with a heavy-duty stand mixer fitted with a paddle attachment on medium speed until smooth, about 1 minute. With mixer running, add eggs, 1 at a time, beating until combined after each addition. Add brown sugar, sour cream, flour, vanilla, and salt, and beat until just combined, about 2 minutes, stopping to scrape down sides as needed. Pour cream cheese mixture into prepared crust.
Place springform pan in large roasting pan. Pour enough hot water into roasting pan to come 1 inch up sides of pan. Bake cheesecake at 350°F until just set in center and top is slightly puffed and jiggles from side to side, 45 to 50 minutes. Turn off oven; keep door closed. Let cheesecake stand in oven 45 minutes. Remove cheesecake from roasting pan; remove and discard foil from springform pan. Refrigerate uncovered until cold, about 3 hours. Cover and refrigerate 8 hours or up to overnight.
Prepare the Topping: Melt butter in a large skillet over medium-high. Stir in brown sugar and cinnamon, and bring to a boil. Stir in apples. Cook, stirring occasionally, until apples are just tender, about 6 minutes. Remove from heat, and let cool 30 minutes. Spoon apples over chilled cheesecake, and drizzle with caramel from skillet. Slice and serve.