Preheat your oven to 350°F. While it heats, generously grease a 9x13 inch baking dish (or similar 3-quart dish) with butter or cooking spray. This prevents the cobbler from sticking and ensures even browning on the edges.
Pour the melted and slightly cooled butter directly into the prepared baking dish. In a separate bowl, whisk together the Bisquick baking mix, milk, and salt until you have a thick, drop-biscuit batter with a few small lumps remaining—don't overmix or the topping will be tough. Pour this batter evenly over the butter in the dish, but do not stir it together yet. I like to leave the batter slightly loose on top because it will naturally incorporate with the fruit juices as it bakes, creating a wonderfully moist cobbler.
In a bowl, combine the drained sliced peaches with sugar, cinnamon, nutmeg, salt, vanilla extract, and fresh lemon juice. Stir gently until the peaches are evenly coated and the sugar begins to dissolve slightly. The lemon juice brightens the peach flavor and prevents the cobbler from tasting overly sweet.
Pour the peach mixture and its juices evenly over the batter in the baking dish. Gently spread the peaches in a single layer, but do not stir—the batter will rise up around the fruit as it bakes, creating a marbled, rustic appearance. Place the dish in the preheated 350°F oven and bake for 35-40 minutes, until the top is golden brown and a toothpick inserted into the biscuit portion comes out clean.
Remove the cobbler from the oven and let it rest for 10 minutes before serving. This resting time allows the filling to set slightly and makes serving much easier. The cobbler will continue to firm up as it cools, but is best enjoyed while still warm. Serve each portion with a generous dollop of whipped cream or a scoop of vanilla ice cream for a classic finish.