In a large bowl, mix berries with sugar, cornstarch, thyme leaves and lemon juice until the fruit is evenly coated. Transfer to a 2-qt. baking dish.
In a medium bowl, whisk the flour, 1/4 cup sugar, baking powder and salt. Combine 3/4 cup plus 3 tbsp. cream with thyme and lemon zest and mix into dry ingredients just until the dough comes together.
Using a spoon, dollop the dough in craggy mounds, spacing evenly on top of the berry mixture. Dab the biscuits with cream, then sprinkle them with 1 tbsp. sugar. Bake at 400 degrees until the filling bubbles and a toothpick inserted into the biscuits comes out clean, tenting with foil if the biscuits are browning too quickly, 35 to 40 minutes.