In a large bowl, mix strawberries with sugar, cocoa powder, cornstarch and vanilla extract until the fruit is evenly coated. Transfer to a 2-qt. baking dish.
In a medium bowl, whisk the flour, sugar, chocolate chips, baking powder, and salt. Add cream and mix just until the dough comes together.
Pat into a 1/2-inch-thick round. Using a cookie cutter, cut out biscuits; arrange on top of the strawberry mixture. Brush 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.