Wash peaches, peel using the blanching method, halve, remove pits, and dice into 1/2-inch pieces. Toss with brown sugar and set aside.
Combine sliced peaches, sugar, water, lemon juice, and cinnamon in a saucepan over medium heat. Cook for 8-10 minutes until tender and syrupy. Set aside and keep warm.
In a large bowl, whisk together flour, granulated sugar, baking powder, baking soda, cinnamon, and salt until well combined.
In a separate bowl, beat eggs lightly, then whisk in buttermilk, melted butter, and vanilla extract until smooth and fully combined.
Pour wet ingredients into dry and gently fold with a whisk or spatula until no large streaks of flour remain (about 10-15 strokes). Allow batter to rest, uncovered, for 5 minutes.
Gently fold the brown sugar-tossed peaches and any collected juice into the rested batter using a rubber spatula, using 3-5 folds to distribute evenly without overmixing.
Preheat griddle over medium heat until drops of water dance and evaporate in 2-3 seconds. Grease with butter or oil, spreading evenly.
Pour 1/4 cup of batter per pancake, spacing 2 inches apart. Cook until bubbles form across the surface and edges look set, about 2-3 minutes. Flip and cook another 1-2 minutes until golden brown.
Stack pancakes on a serving plate, spoon warm peach syrup over the top, add a pat of butter, and garnish with fresh peach slices, powdered sugar, or maple syrup. Serve immediately.