In a large bowl, combine the peaches, lemon juice, vanilla, cinnamon, nutmeg, and salt. In a separate small bowl, whisk together the sugar and flour, then add this dry mixture to the peaches and gently toss until the peaches are evenly coated. The lemon juice prevents browning while the spices and sugar begin to draw out the peaches' natural juices. Let this sit for a few minutes while you prepare the batter.

Preheat your oven to 375°F. While it heats, pour the peach mixture from Step 1 into a 9x13 inch baking dish (or similar size), spreading it evenly across the bottom. The oven preheating while you assemble ensures you're ready to bake immediately after the batter is mixed.

In a medium bowl, whisk together the room-temperature eggs, sugar, and melted butter until well combined and slightly pale, about 1-2 minutes. Pour in the milk and vanilla, whisking until smooth. I find that using room-temperature eggs ensures the batter mixes smoothly without lumps and creates a more tender crumb in the final cobbler.

In another small bowl, whisk together the flour, baking powder, and salt. Gently fold this dry mixture into the wet batter from Step 3 until just combined—don't overmix, as some small lumps are fine and will keep the cobbler topping tender. The batter should be thick but pourable.

Pour the batter from Step 4 evenly over the peaches in the baking dish, spreading gently with a spatula to cover most of the fruit. Sprinkle the coarse sugar over the top—this creates a beautiful, slightly crunchy texture as it bakes. Place the dish in the preheated 375°F oven and bake for 35-40 minutes, until the topping is golden brown and a toothpick inserted into the batter (not the fruit) comes out clean. The cobbler will have a cake-like topping with bubbling fruit around the edges.

Remove the cobbler from the oven and let it rest for 5-10 minutes before serving. This brief resting period allows the filling to set slightly and makes serving easier. I like to serve it warm with a scoop of vanilla ice cream or fresh whipped cream to complement the warm spiced peaches.