Heat oven to 375ºF.
In a mixing bowl, combine the peaches, brown sugar, flour, salt, and vanilla. Mix to combine, then pour into a 9"x9" or 6"x4" pan. Tent with foil and bake 20 minutes, or until soft and juicy.
Meanwhile, in the same mixing bowl, combine the cookie crumbs, baking soda, baking powder, and salt. Mix well. Cut in the butter until the mixture resembles wet sand – the butter should be very small and uniform, but still visible. Add the milk and stir until combined.
Drop tablespoons of dough on top of the cooked peaches. Return to the oven and bake another 35-50 minutes, or until browned and cooked through.
Let cool 30 minutes before serving.