Combine flour, sugar, baking powder, baking soda, and salt in a large bowl. Beat buttermilk, milk, eggs, and melted butter together in a separate bowl. Keep the two mixtures separate until you are ready to cook.

Heat a lightly oiled griddle or frying pan over medium-high heat. You can flick water across the surface and if it beads up and sizzles, it's ready.

Pour the wet mixture into the dry mixture; use a wooden spoon or fork to mix until it's just blended together. The batter will be a little lumpy which is what you want.

Pour or scoop batter onto the preheated griddle, using approximately 1/2 cup for each pancake. Cook until bubbles appear on the surface, 1 to 2 minutes; flip with a spatula and cook until browned on the other side. Repeat with remaining batter.