Heat griddle to 375 degrees f. Whisk together flour, baking powder, baking soda, salt, and sugar in a medium bowl. Add eggs, buttermilk, and 4 tbsp melted butter; whisk to combine. Do not overmix. Batter should have small to medium lumps
Heat oven to 175 degrees f. Test griddle by sprinkling a few drops of water on it. If water bounces and spatters off the griddle, it is hot enough. Using a pastry brush, brush remaining 1/2 tsp butter onto the griddle. Wipe off excess with a paper towel.
Using a 4-ounce ladle (about 1/2 cup) pour pancake batter in pools two inches away from one another. When pancakes have bubbles on top and are slightly dry around the edges (about 2 1/2 minutes) flip over. Cook until golden on the bottom, about 1-2 minutes.
Repeat with remaining batter, keeping finished pancakes on a heat-proof plate in the oven. Serve with your favorite condiments.