Add sliced peaches to a mixing bowl. Add sugar and lemon juice and stir a couple of times. Rest for 3 minutes. Stir again. Rest for another 3 minutes. The sugar will help bring out the juice from the peaches, so continue to stir and rest, as needed, until you have about ⅓ cup peach juice.
Strain peach juice into a small saucepan. Set peaches aside.
Mix cornstarch and water together until smooth. Add to the saucepan with the peach juice. Stir well.
Cook over medium heat, stirring, until thickened.
Lightly dust a piece of parchment or wax paper with flour. Roll out pie crust into a large circle, 11-12’’ in diameter.
Add the sauce from saucepan (it should be pretty thick) back to the bowl with the peaches and toss to coat.
Use a slotted spoon to layer the peaches into the center of the rolled out pie crust, leaving any excess sauce in the bowl. Top with blackberries.
Gently fold the outer edge of the crust up and over the fruit, overlapping as needed to form a circle.
Brush a light egg wash on the edges of the crust. Sprinkle lightly with sugar.
Bake at 425 degrees F for 35-40 min. or until the crust is golden brown. Depending on how juicy your peaches are, you may want to check the tart while baking. If you see pools of juice threatening to leak out of the crust you can use a paper towel to blot the juice out.
Cool for a few minutes before cutting into slices. Serve warm, with vanilla ice cream, if desired.