Whisk together flour, sugar, baking powder, baking soda, and salt in a large bowl. In another bowl, mix buttermilk, egg, and melted butter, then combine with the dry ingredients until smooth.
Stir brown sugar, melted butter, and cinnamon in a small bowl and transfer to a piping bag or zip-top bag with the corner snipped.
Heat a nonstick skillet or griddle over medium heat and lightly grease. Pour ¼ cup batter onto the hot surface, pipe a swirl of cinnamon mixture on top, and cook 2–3 minutes until bubbles form. Flip gently and cook 1–2 minutes until golden.
Whisk powdered sugar, milk, and vanilla until smooth. Stack pancakes, drizzle with glaze, and serve warm.