Preheat the oven. Preheat the oven to 350°F. Place a baking sheet on the lower oven rack to catch any bubbling fruit juices.
Make the lavender lemon sugar. In a small bowl, combine the sugar, lemon zest, and lavender (if using). Use your fingertips to rub everything together until fragrant.
Prepare the fruit filling. In a large bowl, combine the blueberries, peaches, cornstarch, lemon juice, and vanilla. Add the lavender lemon sugar and toss until evenly coated. Transfer the fruit mixture to a baking dish.
Make the biscuit topping. In another bowl, whisk together the flour, sugar, and baking powder. Add the cubed butter and use your fingertips or a pastry cutter to work the butter into the flour until the pieces are about pea-sized.
Mix the dough. Stir in the heavy cream and vanilla until a thick, shaggy dough forms. Be careful not to overmix.
Assemble the cobbler. Dollop spoonfuls of biscuit dough evenly over the fruit filling. In a small bowl, mix the remaining sugar and lavender together (if using) and sprinkle over the biscuit topping. Brush the tops with heavy cream.
Bake. Bake for 55 minutes to 1 hour, until the fruit is bubbling and the biscuit topping is lightly golden brown.
Cool and serve. Let the cobbler rest for at least 20 minutes before serving. Enjoy warm as is or with vanilla ice cream.