Preheat oven to 400° F.
Add filling ingredients EXCEPT brown sugar (basically, your peaches, sugar, lemon juice, flour salt, nutmeg, cinnamon and vanilla extract) to a large bowl and stir gently to combine.
Grease an 8x8 baking pan. Add peach mixture in an even layer. Sprinkle brown sugar over the top and bake for 10 minutes.
In the meantime, add flour, ½ cup sugar, salt and baking powder into a medium bowl and stir to combine. Chop the butter into small pieces. Add them to the bowl and use your fingertips or a pastry cutter to work them into dough until pea sized pieces are formed. (See notes for alternative method).
Add the heavy cream and flour to the mixture and mix until just combined. Do not overmix.
Remove the baking pan from the oven after 10 minutes. Carefully spoon the dough over the top. It doesn't have to cover everything, that's why this is a "cobbler"!
Place the cobbler into the oven and bake for 10-15 minutes until the topping begins to brown.
This step is part way optional. But if you give the top a brush (or a dab) with egg wash and a sprinkle of sugar, it will look extra pretty when it comes from the oven as it finishes baking.
Oh, and an egg wash is just some egg white mixed with a little liquid - or in this case water. It gives the cobbler a glossy finish and also gives the sugar sprinkled on top something to adhere to.
I say it's worth the extra effort. But if you choose to forgo this step, you'll need to still cook the cobbler for another 10-15 minutes or so until the top is golden brown and the peaches are bubbly.
Let it cool slightly before topping with ice cream or whipped cream.