01 -  Preheat oven to 350°F. Line a standard 12-cup muffin tin with paper liners. 
 02 -  Whisk flour, granulated sugar, baking powder, baking soda, salt, and chai spices in a large bowl. In a separate bowl, combine vegetable oil, milk, egg, and vanilla extract. Stir wet ingredients into dry mixture until just blended. 
 03 -  Beat cream cheese and granulated sugar with an electric mixer until smooth. Incorporate egg and vanilla, mixing until creamy and uniform. 
 04 -  Add one heaping tablespoon of chai cake batter into each muffin liner. Top with one tablespoon of cheesecake mixture, then another layer of chai cake batter to fill each liner about three-quarters full. 
 05 -  Bake muffins for 20 to 22 minutes, or until a toothpick inserted into the cake portion comes out clean. Transfer muffins to a wire rack and cool completely. 
 06 -  Melt unsalted butter in a skillet over medium heat. Add diced apples, brown sugar, ground cinnamon, and lemon juice. Cook, stirring constantly, until apples are tender and caramelized, approximately 5 to 7 minutes. Let cool. 
 07 -  Slice each cooled muffin horizontally into two even rounds. 
 08 -  For each skewer, alternate threading a muffin slice, a spoonful of apple filling, and a drizzle of caramel sauce, repeating for two to three layers. Finish with extra caramel and a light sprinkle of chai spice, if desired. 
 09 -  Serve immediately, or refrigerate skewers for 15 minutes for a firmer set.