Plug in your Belgian waffle maker and set it to a medium-high heat setting. Let it fully preheat while you mix the batter, about 5 minutes, and lightly grease the plates if needed.
In a large bowl, whisk together the flour, granulated sugar, baking powder, baking soda, salt, ground cinnamon, and ground nutmeg for about 30 seconds until evenly distributed.
In a second bowl, beat the eggs lightly, then pour in the buttermilk, melted and slightly cooled butter, and vanilla extract. Whisk until smooth and uniform.
Pour the wet ingredients into the dry ingredients and stir gently with a silicone spatula until just combined. Stop while a few small lumps remain; the batter should be thick and pourable.
Pat the diced peaches dry with paper towels, add them to the batter, and fold gently until evenly spread. If the peaches are very juicy, dust them with a little flour first.
Spoon about 3/4 cup (180ml) of batter onto the center of the hot iron and cook for 4 to 5 minutes, until the steam slows and the waffle is deep golden brown. Transfer to a wire rack.
Serve the waffles warm with a drizzle of pure maple syrup and extra sliced fresh peaches. Add butter or whipped cream if desired and serve promptly.