Prepare the Cinnamon Filling: In a small bowl, mix the melted butter, brown sugar, cinnamon, and vanilla extract until smooth. Transfer the mixture to a piping bag or zip-top bag. Let it cool slightly until thick enough to pipe without spreading too quickly.
Mix the Dry Ingredients: In a large bowl, whisk together the flour, granulated sugar, baking powder, baking soda, and salt until evenly combined.
Combine the Wet Ingredients: In another bowl, whisk the egg, buttermilk, melted butter, and vanilla extract until smooth. Pour the wet mixture into the dry ingredients and stir gently until just combined. Do not overmix.
Make the Cream Cheese Glaze: Beat the softened cream cheese and butter until creamy. Add the powdered sugar and vanilla extract, then mix until smooth. Add milk gradually until the glaze reaches a pourable consistency. Set aside.
Heat the Skillet: Place a nonstick skillet or griddle over medium-low heat. Lightly grease it with butter. Allow the surface to warm evenly before adding the pancake batter.
Cook the Pancakes with Cinnamon Swirls: Pour about ¼ cup of pancake batter onto the skillet. Once the surface begins to set slightly, pipe a spiral of cinnamon filling over the pancake, starting near the center and moving outward. Leave a little space around the edges.
Flip and Finish Cooking: Cook for about 2–3 minutes, until bubbles appear and the edges look set. Carefully flip the pancake and cook for another 1–2 minutes. The cinnamon filling may caramelize, so keep the heat moderate to prevent burning.
Add the Glaze and Serve: Transfer the cooked pancakes to a serving plate with the cinnamon swirl facing up. Drizzle with cream cheese glaze and serve warm.