5 small to medium gala apples (2 lbs. total)
1 stick (4 oz.) unsalted butter
1 cup plus 1 Tbsp. sugar
1 Tbsp. fresh lemon juice
8 graham cracker squares, finely chopped
1/8 tsp. salt
11 oz. cream cheese, at room temperature
1 tsp. vanilla extract
1 cup walnuts, chopped
Whipped cream, for topping
Peel, quarter and core the apples. Cut each quarter into 3 lengthwise slices. In a large nonstick skillet, melt 3 Tbsp. butter over medium-high heat. Add the apples, 6 Tbsp. sugar and the lemon juice. Cook, turning occasionally, until the apples begin to caramelize, about 8 minutes. Lower the heat to low, add 1 Tbsp. butter and cook until the apples are tender, about 5 minutes. Cool.
Line 6 cups of a jumbo muffin pan with jumbo liners and preheat the oven to 325°. In a small pan, melt 2 Tbsp. butter, then place in a medium bowl. Mix in the graham crackers and salt. Divide the mixture among the muffin cups. Press into the bottoms with a narrow drinking glass. Transfer to the freezer to set.
In a bowl, combine the cream cheese and 1/2 cup sugar. Using a mixer, beat at high speed until creamy, about 2 minutes. Beat in the eggs 1 at a time, scraping down the bowl twice, until blended. Mix in the vanilla.
Arrange 5 apple slices in a single layer on the crust in each muffin cup. Reserve the remaining apples with their juices at room temperature in a covered bowl. Divide the cream cheese mixture evenly among the cups; bake until set but slightly jiggly, about 20 minutes. Turn off the oven, open the door slightly and let cool for 30 minutes. Refrigerate for at least 5 hours or overnight.
In a small skillet, melt the remaining 2 Tbsp. butter over medium heat. Add the walnuts and 2 tbsp. sugar and cook, stirring, until toasted, 4 to 5 minutes. Cool on paper towels, then break up the candied nuts.
Arrange the reserved apples with their juices on top of the cakes. Top the cakes with whipped cream and the candied nuts.