Peel and dice the peaches into 1/4-inch pieces. Pat them dry with paper towels and set aside.
In a large mixing bowl, whisk together the flour, sugar, baking powder, baking soda, and salt until evenly combined.
In a separate bowl, whisk the buttermilk, eggs, melted butter, and vanilla extract until smooth and well blended.
Pour the wet ingredients into the dry ingredients and gently fold together with a spatula until just combined. The batter should be slightly lumpy — do not overmix.
Gently fold the diced peaches into the batter, distributing them evenly throughout.
Heat a griddle or large nonstick skillet over medium heat and lightly grease with butter or oil. Test the temperature by sprinkling a few drops of water — they should sizzle immediately.
Pour 1/4 cup of batter onto the griddle for each pancake, spacing them 2 inches apart. Cook until bubbles form on the surface and the edges look set, about 2-3 minutes.
Flip the pancakes carefully with a wide spatula and cook for another 1-2 minutes until golden brown and cooked through.
Transfer finished pancakes to a plate and keep warm. Repeat with remaining batter, adding more butter or oil to the griddle as needed.
Serve immediately with maple syrup, whipped cream, or additional fresh peach slices.
