Start by making the pie crust, whisking together flour, brown sugar, and salt in a large bowl. Then, grate in cold butter, and toss it into the mixture.
Roll the chilled dough out on a floured sheet of parchment so that it's about 1/4" thick. Use a small cookie cutter to cut the dough into individual pieces.
Before baking, brush the pie crust with an egg wash made from a combination of egg white and water. This will help the cobbler topping brown as it bakes.