01 - Preheat oven to 350°F. Line a 12-cup muffin tin with paper liners.
02 - In a mixing bowl, combine flour, sugar, baking powder, baking soda, salt, and chai spice blend. In a separate bowl, whisk together vegetable oil, whole milk, egg, and vanilla extract. Combine wet and dry ingredients until just mixed.
03 - In a separate bowl, beat softened cream cheese with granulated sugar using an electric mixer or whisk until smooth. Add egg and vanilla extract; blend until creamy.
04 - Fill each muffin cup with a heaping tablespoon of chai cake batter. Add one tablespoon of cheesecake mixture on top, then repeat with another layer of chai cake batter. Fill cups to about three-quarters full.
05 - Bake for 20 to 22 minutes, or until a toothpick inserted into the cake comes out clean. Cool muffins completely on a wire rack.
06 - In a skillet over medium heat, melt unsalted butter. Add diced apples, brown sugar, cinnamon, and lemon juice. Cook, stirring frequently, until apples are caramelized and tender, about five to seven minutes. Remove from heat and allow to cool.
07 - Once cooled, slice each muffin horizontally into two even rounds.
08 - On each skewer, thread a slice of muffin, spoonful of apple filling, and drizzle of caramel sauce. Repeat to create two to three layers, finishing with a drizzle of caramel and a sprinkle of chai spice if desired.
09 - Serve immediately, or for firmer texture, chill assembled skewers for fifteen minutes before serving.