In a large bowl, gently toss together the strawberries, blueberries, sugar, cornstarch, lemon zest, and ginger. Place the mixture in a shallow 10-cup baking dish.
To make the biscuits: In another large bowl, whisk together the flour, sugar, baking powder, and baking soda. Cut the butter into the flour using a dough blender or your fingers, until it resembles coarse cornmeal. Stir in the Cheddar.
In a small bowl, combine the egg, buttermilk, and cream. Add this to the flour mixture and stir just until there is no more visible flour, but the dough should still be sticky and lumpy.
Scoop the biscuits evenly over the berries. They will be about golf-ball-sized scoops.
Bake until the biscuits are golden brown and baked through, about 40 minutes. (See Cook’s Note.)