Preheat your oven to 350°F. In a large bowl, toss your 4 cups of sliced peaches with both sugars, cinnamon, nutmeg, and lemon juice. Let it sit for five minutes—the peaches will start releasing their juice and that's exactly what you want. Pour the whole mixture (including all the juices) into a 9x13-inch baking dish.
In another bowl, whisk together your flour, baking powder, and salt until combined. This prevents lumps in your batter later. Set it aside for a second.
Crack your 2 eggs into a medium bowl and beat them lightly. Add the milk and melted butter, stirring until everything's mixed. Pour this wet mixture into your dry ingredients and stir just until combined—don't overmix or your topping gets tough.
This part's kinda magical: pour the batter right over the peaches in the baking dish. Don't stir it! The batter will look like it's sitting on top, but trust me on this—it'll settle and bake perfectly. Sprinkle the vanilla bean seeds over the top.
Slide the dish into your preheated oven and bake for 40-45 minutes. You'll know it's done when the topping turns golden brown and you see the fruit bubbling around the edges. My first attempt I walked away for two minutes and almost missed seeing that gorgeous bubbly moment.
Let it cool for about 10 minutes before serving. I know it's hard to wait, but this gives everything time to set up slightly. The peach cobbler will still be warm and wonderful, just easier to scoop.
Serve each portion warm with vanilla ice cream or whipped cream. The contrast between the warm fruit filling and cold cream is honestly perfection. You can definitely make this fruit cobbler ahead and reheat it gently.