In a medium saucepan, combine apples, lemon juice, light brown sugar, butter, spices and salt. Cook over medium heat for 12 minutes, stirring occasionally. Set aside and cool for 10 minutes.
Transfer 3/4 of the apples to a medium bowl. Cool completely. Cover with plastic wrap and chill in the fridge. For the rest of the apples, add to a food processor and process into a puree (about ¾ cup). The puree should be pretty thick. Transfer to a small bowl to cool completely.
Preheat oven to 325°F (165˚C). Lightly butter a 9 x 13 metal baking pan. Line with 2 parchment papers (1 lengthwise & 1 crosswise), leaving some overhang on all sides, then butter the parchment papers again.
For the crust, in a large bowl, whisk together graham cracker crumbs and sugar. Add the melted butter and mix everything together. Press the mixture firmly onto the bottom of the prepared pan. Bake in the oven for 5 minutes. Remove from oven and cool on a cooling rack.
For the filling, in a large mixing bowl with an electric mixer fitted with a paddle attachment, add cream cheese. Beat at medium speed until smooth and fluffy, about 3 minutes. Add sugar and beat to combine. Add sour cream and vanilla extract, and mix well. Add eggs and beat on medium-speed until smooth, scraping down the sides of the bowl a couple times. Do not overmix. Pour the filling into the cooled baking pan.
To make the apple spots, using a small spoon, start with ½ of the puree. Scoop about ½ teaspoon of puree and drop them all over the cheesecake filling. With a toothpick or skewer, draw through the dollops of puree a few times to blend. It’s ok if the puree sinks at this point. Then, drop the other ½ of the puree. This time, do not draw through the dollops as much, so the puree stays more intact and remains visible on top.
Carefully transfer the baking pan to the oven and bake for 40 – 43 minutes, until the edges are slightly puffed and the middle is slightly wobbly (when you shake the pan). Do not overbake. Remove from oven and transfer to a wire rack on stovetop and let cool completely, about 3 hours. Putting the cheesecake near the oven will prevent the cheesecake to cool too quickly, which can help to reduce cracks.
Chill the cheesecake in the fridge until cold, at least 2 hours.
When ready to serve, gently use the parchment paper overhangs to lift the entire cheesecake out of the pan. Place on a cutting board and cut into 12 big squares or 24 small squares. Transfer to serving plates, top with the sautéed apples and serve.