Prepare the cream cheese topping by whipping together the softened cream cheese, milk, and butter using a stand mixer on low speed. Slowly add the confectioners sugar and mix until smooth. Set aside.
Prepare the cinnamon mixture by mixing together the butter, brown sugar, cinnamon, and nutmeg in a small bowl. Transfer to a squeeze bottle and set aside.
In a medium bowl, combine the milk and white vinegar. Set aside and allow the mixture to sit for 5 minutes.
In a small bowl, combine the flour, baking powder, baking soda, and salt. Set aside.
Add the egg and butter to the milk and stir until just combined. Add the flour mixture to the wet ingredients and stir until the lumps have dissolved.
Heat a griddle or large skillet over medium heat. Spray the griddle and cookie cutter with cooking spray. Place the cookie cutter onto the griddle and add a few spoonfuls of batter (the amount of batter depends on the size of the cookie cutter). Drizzle the cinnamon mixture over the batter. Cook until bubbles appear on the surface, then remove the cookie cutter and flip the pancake with a spatula. Cook until lightly browned and the pancake is cooked through. Repeat with remaining batter. Drizzle the cream cheese topping or chocolate syrup over the pancakes and serve.