Preheat your grill or grill pan over medium-high heat. In a bowl, combine the mixed berries, granulated sugar, lemon juice, and olive oil. Toss gently to coat and set aside to marinate for about 10 minutes.
In a separate bowl, whisk together the flour, baking powder, and salt. Add the cold cubed butter and mix with your fingers or a pastry cutter until the mixture resembles coarse crumbs.
Pour in the milk and vanilla extract, stirring until just combined. Do not overmix. Turn the dough out onto a floured surface and gently knead it a few times until it comes together.
Pat the dough into a 1-inch thick round and cut out shortcakes using a biscuit cutter or a glass. Place the shortcakes on a baking sheet lined with parchment paper.
Grill the marinated berries for about 3-4 minutes, turning occasionally until they are slightly charred and softened. Remove from the grill and set aside.
While the berries are grilling, bake the shortcakes in the oven at 400°F for 15-20 minutes or until golden brown.
In a mixing bowl, whip the heavy cream, powdered sugar, and vanilla extract until soft peaks form.
To assemble, split the warm shortcakes in half, layer with charred berries, and top with a generous dollop of whipped cream. Replace the top half of the shortcake and serve immediately.