Preheat the oven to 400°F (200°C).
Wash, pit, and slice the peaches into approximately ¾-inch wedges.
In a large mixing bowl, combine the peaches, brown sugar, lemon juice, cornstarch, kosher salt, nutmeg, cinnamon, and vanilla extract. Stir gently until the peaches are evenly coated.
Divide the butter between two 6-inch cast-iron skillets or melt it in one large 10- or 12-inch oven-safe skillet.
Add the peach mixture and all of the juices to the prepared skillet.
Bake for 10 to 15 minutes until the peaches begin to soften and release their juices.
Remove the skillet from the oven.
Arrange the refrigerated biscuit dough evenly over the warm peaches, leaving a little space between each biscuit.
Reduce the oven temperature to 375°F (190°C).
Return the skillet to the oven and bake for about 20 minutes until the biscuits become puffed and lightly golden.
Sprinkle the tops with a little cinnamon and brown sugar if desired.
Bake for another 5 minutes until the biscuits are deeply golden and fully cooked.
Allow the Peach Cobbler with Old Fashioned Vanilla Ice Cream to cool for at least 5 minutes before serving.
Serve warm with generous scoops of old fashioned vanilla ice cream and an extra dusting of cinnamon.