In a large bowl, combine flour, brown sugar, baking powder, and salt. Mix well, breaking up any brown sugar clumps with a fork.
Make a well in the center. Add eggs and milk. Lightly whisk the eggs into the milk before incorporating the dry ingredients.
Add melted butter and vanilla. Mix from the outside inward until the batter is smooth with no visible clumps. Do not overmix.
Heat a non-stick skillet over medium heat or preheat an electric griddle to 300°F.
Lightly grease the surface with oil or butter.
Pour ¼ cup of batter onto the pan. Gently spread slightly if needed.
Cook for about 2 minutes, until bubbles form and edges look set. Flip and cook another minute until golden brown.
Repeat with remaining batter. Keep pancakes warm on a plate.
Serve Brown Sugar Pancakes warm with maple syrup, cinnamon, or fresh berries.