Heat the cream in a sauce pan. Stir occasionally to keep skin from forming. Just before it is boiling, remove from heat and add vanilla.
Meanwhile, cream egg yolks and sugar in a bowl. Try not to incorporate any air into the mix. I find that a fork works well for this small amount -- a whisk is too big.
SLOWLY drizzle cream into eggs, continuing to mix with the fork. If you pour too quickly you will cook the egg. Again, try not to incorporate any air as you mix.
Drain the peaches and place peach slices in the bottom of each ramekin. Then pour the custard on top of the peaches. You want to have enough custard that the peaches are completely covered. Narrower, taller ramekins work better than wider, shorter ones.
Place ramekins in a baking tray or roasting pan, then pour water into the pan (don't splash into the custard) so that it comes halfway up the sides of the ramekins. Carefully place in the oven (don't splash into the custard) and bake about 30 minutes. Custard is done when it is set but still jiggles.
Remove from the oven, and remove from the water bath. Allow to cool completely. Then cover with plastic wrap and chill for a couple hours in the fridge. You can store like this for several days if you like.
Just before serving, sprinkle a thin layer of brown sugar on top of each custard and use a kitchen torch (or your oven's broiler) to melt and caramelize the sugar. Try not to burn it. If you are using the broiler, be careful, it burns very quickly. Don't take your eyes off of it!