In a bowl, sift together the flour, baking powder, baking soda, and salt. In another bowl, beat together the eggs and buttermilk. Pour into the dry ingredients and mix until a smooth batter forms. Fold in the 4 Tbsp melted butter and the blueberries.
Heat a large frying pan over medium-high heat until hot. Brush with melted butter. For each pancake, ladle 2 Tbsp of the batter into the pan, forming circles 4–5 inches (10–13 cm) in diameter. Cook until bubbles form on the surface, about 3 minutes. Turn the pancakes and cook until lightly browned on the second sides, about 3 minutes. Transfer to a platter. Repeat until all the batter is used, brushing the pan with more butter as needed. Serve the pancakes right away.