Prepare the cinnamon swirl: In a small bowl, mix the melted butter, brown sugar, and ground cinnamon until smooth. Transfer the mixture to a piping bag or small resealable bag and snip off a tiny corner.
Make the pancake batter: Whisk together the flour, granulated sugar, baking powder, and salt in a large bowl. In another bowl, whisk the milk, eggs, vanilla extract, and melted butter. Add the wet ingredients to the dry ingredients and gently mix until just combined. Do not overmix.
Heat the skillet: Place a nonstick skillet or griddle over medium-low to medium heat. Lightly grease the surface with butter.
Add the pancake batter: Pour the batter onto the hot skillet to form a round pancake. Cook until bubbles begin to appear on the surface and the edges start to look set.
Add the cinnamon swirl: Pipe the cinnamon mixture over the pancake in a spiral, starting from the center and working outward. Leave a little space around the edges.
Flip and cook: Carefully flip the pancake with a spatula and cook the other side until golden brown and cooked through. Repeat with the remaining batter.
Make the vanilla glaze: Whisk the powdered sugar, milk, and vanilla extract in a small bowl until smooth. Add a little more milk if needed to reach a drizzle-friendly consistency.
Stack and serve: Stack the warm cinnamon roll pancakes on a plate and drizzle generously with the vanilla glaze. Serve immediately with your favorite toppings.