In a large bowl, whisk together the all‑purpose flour, packed brown sugar, baking powder, and salt until evenly combined.
In a separate bowl, whisk the eggs and milk together. Add the melted butter and vanilla, stirring to combine the wet ingredients.
Pour the wet ingredients into the dry mixture. Stir gently from the outside in until just combined; the batter should be slightly lumpy.
Heat a non‑stick skillet or griddle over medium heat. Grease lightly with butter or oil.
Pour about ¼ cup of batter onto the heated surface for each pancake. Cook until bubbles form on top and edges look set, about 2 minutes.
Flip and cook for another 1–2 minutes until golden brown and cooked through.
Remove and keep warm while you cook the remaining batter.