Preheat oven to 400F with the rack positioned in the center.
Grease an 8” x 8” or 9" x 9" high-sided baking dish.
Peel and chop the peaches into 2-inch slices or chunks.
Add peaches, white sugar, lemon juice, flour, salt, nutmeg, cinnamon, and vanilla extract to a large glass bowl.
Thoroughly mix ingredients and then transfer them to the pan.
Sprinkle mixture with an even layer of the brown sugar before placing the pan in the oven.
Bake for 10 minutes.
While peaches are baking, add flour, sugar, salt, and baking powder to a different bowl and stir to combine.
Cut the cold butter into very small pieces with a sharp knife then add to the bowl with dry ingredients.
With clean fingers, massage the butter with the drys until pebble-sized dough forms.
Add heavy cream and water to the flour mixture and stir with a fork until all the dry ingredients are moist and somewhat sticky. Don't overwork the dough.
Carefully remove the pan of peaches from the oven; dollop spoonfuls of the dough mixture on top of the hot peach mixture.
Bake for an additional 30–40 minutes, until the crust is golden brown and the peach mixture bubbles at the edges.
Remove from the oven and let the pan of cobbler rest for 10–15 minutes.
Serve warm, ideally with a scoop of vanilla ice cream or whipped cream.
To store: Refrigerate in an airtight container for up to 4 days. To reheat: Preheat oven to 325 °F, cover cobbler with foil, and bake ~15 minutes or until heated through.