For the filling:
3 cups blackberries
1 tablespoon sugar (use more if your fruit is particularly tart)
2 1/2 cups chopped peaches
1/2 teaspoon almond extract
For the biscuits:
1 cup all purpose flour
1 1/2 teaspoons baking powder
1/2 teaspoon salt
1 tablespoon sugar, plus additional 2 tablespoons sugar for sprinkling
1 cup sour cream
Preheat your oven to 450 degrees F, position a rack in the bottom third of the oven.
Mix blackberries and sugar in a medium bowl, add peaches and almond extract.
In a large bowl, whisk flour, baking powder, salt, and 1 tablespoon sugar until well blended. Fold in sour cream and stir until incorporated.
Turn out dough onto a floured work surface and shape into a log. Cut the log into eight slices, and pat until about an inch thick.
Pour fruit filling into a deep-dish pie pan and arrange biscuits on top. Sprinkle top with remaining sugar, then place the pie pan on a cookie sheet to catch drips.
Bake 25 minutes on lower rack of the oven, until the top is golden.
Let cool 10 minutes before serving.