In a large bowl, whisk together the flour, sugar, baking powder, baking soda, and salt until evenly combined.
In a separate bowl, whisk the buttermilk, milk, eggs, melted butter, and vanilla until smooth.
Pour the wet ingredients into the dry ingredients and gently stir with a wooden spoon or spatula until just combined; a few lumps are fineādo not overmix.
Fold in the chocolate chips until evenly distributed.
Heat a lightly greased griddle or large skillet over medium-high heat. Spoon or pour about 1/2 cup of batter per pancake onto the hot surface.
Cook the first side for about 2 1/2 to 3 minutes, until bubbles form on the surface and edges look set, then flip and cook the second side for about 1 1/2 minutes until golden brown.
Transfer cooked pancakes to a plate and keep warm if desired, then repeat with remaining batter and serve warm.