In a large bowl, whisk together the flour, baking powder, baking soda, and salt until well combined.
In another bowl, mix the sourdough starter, milk, eggs, melted butter, and vanilla extract until smooth.
Pour the wet ingredients into the dry ingredients and gently stir until just combined. Be careful not to overmix; a few lumps are okay.
Heat a non-stick skillet or griddle over medium heat and add a little butter or oil to coat the surface.
Pour about 1/4 cup of batter onto the skillet for each pancake. Cook until bubbles form on the surface and the edges look set, about 2-3 minutes.
Flip the pancakes and cook for another 1-2 minutes until golden brown and cooked through.
Repeat with the remaining batter, adding more butter or oil to the skillet as needed.
Serve warm with your favorite toppings such as maple syrup, fresh fruit, or yogurt.