Peel and cut 2 Granny Smith apples into uneven 1/3-inch cubes. Combine them with light brown sugar, lemon juice, cornstarch, cinnamon and 1 tablespoon unsalted butter over medium-low heat around 300°F. Stir from the bottom every 30 seconds for 6 to 8 minutes. Keep the pieces moving so the syrup coats them instead of sticking. Remove them from the heat once the apples soften slightly but still hold their corners. Next, watch for the liquid to change from watery to glossy amber. The cinnamon smell becomes stronger around minute 5 and the syrup should cling lightly to each apple cube. Go past 8 minutes and the apples can collapse into sauce, which makes the cheesecake topping wet. Spread them out and cool for 20 minutes before layering. Cook briefly at moderate heat because partial softening prevents watery fruit from soaking the cheesecake. Preheat the oven to 325°F now so it's fully hot by the time the pan goes in.

Crush the graham crackers into fine crumbs and mix them with granulated sugar and melted unsalted butter. Divide the mixture between 12 paper-lined muffin cups and press each portion into a compact 1/4-inch layer. Bake at 325°F for 5 to 6 minutes. Let the crusts cool for 10 minutes. The Apple Crisp Mini Cheesecake base needs this short bake before any creamy filling goes on top. Then, look for pale golden edges and a surface that feels firm when lightly touched. You should smell toasted graham crackers without any burnt sugar aroma. Bake much longer than 6 minutes and the crusts can harden after chilling. Don't leave loose crumbs along the edges because they'll break away when you peel the liners. Brief baking sets the butter and sugar so the crust stays compact beneath the filling.

Beat room-temperature full-fat cream cheese and granulated sugar for 90 seconds at medium-low speed. Add sour cream and vanilla extract and mix for another 30 seconds. Then add 2 large eggs one at a time and mix only 15 seconds after each addition. Keep every ingredient near 70°F before mixing. Scrape the mixture down once between additions so no dense cream cheese pockets stay hidden around the bottom. The filling should turn thick and glossy with very few visible bubbles. It should fall slowly from the beater instead of pouring like cake batter. Mix longer than about 3 minutes total and excess air can make the centers rise and crack during baking. Stop as soon as the last egg disappears into the mixture. Gentle mixing limits trapped air so the cheesecake sets smooth instead of puffing and collapsing.

Divide the cheesecake filling evenly over the 12 cooled crusts and fill each liner about two-thirds full. Spoon the cooled cinnamon apples over each center without pressing them down. Mix all-purpose flour, old-fashioned rolled oats, light brown sugar, cinnamon and cold cubed unsalted butter until irregular crumbs form. Scatter about 1 tablespoon over each cheesecake. (My first batch had twice the crumble, it buried the apples and baked into a heavy cap.) Next, bake the Apple Crisp Mini Cheesecake cups at 325°F for 19 to 23 minutes. The outer 1/2 inch should look set while the center still gives a small wobble when the pan moves. The oat crumbs turn light golden and a few apple edges deepen to amber. Go past 25 minutes and the filling can turn grainy around the edges. Low oven heat sets the egg proteins slowly so the centers stay creamy.

Cool the muffin pan at room temperature around 70°F for 30 minutes. Then refrigerate the cheesecakes at 40°F or colder for at least 2 hours. Lift out all 12 portions only after the centers feel firm. Peel the paper away slowly from one serving and place it on a small white plate. Cut through the center with one clean downward motion to expose the graham crust, creamy filling and apple layer. Finally, the Apple Crisp Mini Cheesecake should show a firm ivory center with no wet line near the crust. The apple topping stays glossy and the oat crumbs remain craggy rather than soggy. Serve it before it sits above 40°F for more than 2 hours. Skip the chilling window and the filling can slump as soon as you cut it. Chilling firms the cream cheese matrix so the distinct layers hold their shape.