Add peaches, sugar, and 2 tablespoons of flour. Stir to combine until peaches are coated. Set aside.
Turn Instant Pot to Saute setting, add water, and bring to a boil. Add peach mixture to boiling water. Stir and let cook while you prepared the topping.
In another mixing bowl stir together 2 cups of flour, brown sugar, baking powder, salt, nutmeg, and cinnamon.
Cut butter into the dry ingredients using a pastry cutter or a fork until small crumbs form. (It should have a sand-like texture that'll stick together when you pinch it.) Pour in milk and stir until a loose dough forms.
Spoon the cobbler topping over the peaches in dollops. It will spread as the cobbler cooks, but try to evenly cover the peaches as best you can.
Lock the Instant Pot lid in place and set the vent to sealing. Turn the pot to high pressure (Manual setting) and set the timer for 20 minutes.
Once the cooking time is done, allow the pot to naturally release for 10 minutes before quick releasing any remaining pressure.
Portion cobbler into bowls and serve warm with a scoop of vanilla ice cream on top, if you like.