Preheat oven to 400 degrees F. For biscuits, in a medium bowl stir together the first five ingredients (through salt). Using a pastry blender, cut in butter until mixture resembles coarse crumbs. Make a well in the center of flour mixture. Add milk all at once. Using a fork, stir just until mixture is moistened.
Turn dough out onto a lightly floured surface. Knead dough by folding and gently pressing it just until dough holds together. Pat or lightly roll dough into a 3/4inch thick circle. Cut dough into 12 triangles.
For filling, in a large saucepan combine the 1/2 cup sugar, the water, and cornstarch. Add peaches. Cook and stir over medium heat until slightly thickened and bubbly.
Transfer hot filling to a 2-qt. square baking dish. Arrange dough triangles on top of filling.
Bake 20 to 25 minutes or until biscuit topping is golden brown. Serve warm topped with thyme sprigs.