Make the shortcakes: Line a baking sheet with parchment. Combine the flour, sugar, baking powder, and salt in a large bowl and whisk to blend. Using a pastry cutter, fork, or your fingers, cut the butter into the flour mixture until the largest pieces are the pea-size. Combine the cream and vanilla. Make a well in the center of the flour and pour cream into well. Mix with a fork until the dough is evenly moistened and just combined; it should look shaggy and still feel a little dry.
Gently knead by hand in the bowl to create a loose ball. Turn dough out onto a lightly floured surface and pat it into an 8-inch square, ¾ to 1 inch thick. Transfer the dough to the parchment-lined baking sheet, cover with plastic wrap, and chill for 20 minutes.
Meanwhile, preheat the oven to 425°F. Remove the dough from the refrigerator and trim about ¼ inch from each side to create a neat, sharp edge. Cut the dough into 9 even squares (about 2-½ inches square) and spread them about 2 inches apart on the baking sheet. Brush each biscuit with some cream and sprinkle with sugar. Bake until golden brown on top and bottom, about 20 minutes. Set the sheet on a wire rack.
Meanwhile, make the filling: Heat a gas grill or grill pan to medium-high. Slice the peaches into 6 segments per peach. In a small bowl, toss them with the olive oil. Grill the peaches on each side for 2 to 3 minutes without moving them. Remove from the grill and allow them to cool to room temperature. Remove the peels and cut the peaches into smaller pieces, if desired.
In a medium bowl, combine the peaches, blueberries, and liqueur or sugar. Set aside.
Make the topping: Pour the cream into a cold mixing bowl and beat with an electric mixer on medium-high speed until it begins to thicken. Add the sugar and vanilla and beat until soft peaks form when the beaters are lifted.
Assemble and serve: Split the biscuits in half horizontally with a serrated knife. For each serving, set the bottom half of a biscuit on a plate. Scoop about ¾ cup of the fruit and thee juices over the biscuit. Add a generous dollop of whipped cream and cover with the top half of the biscuit.