Preheat the oven to 375 degrees F.
For the filling: In a large bowl, add the peaches, blueberries, dark rum, sugar, cornstarch, ground cinnamon, lemon zest and juice and vanilla extract. Mix well to coat the peaches and blueberries evenly. Set aside.
For the topping: In a large mixing bowl, add the flour, oats, sugar and salt. Add the cold butter cubes and cut the butter into the flour (either with a pastry blender or your hands). Mix until the texture is coarse and clumps in your hand when you squeeze a handful. Add the heavy cream and mix just until the dough just comes together a bit more.
Pour the filling in a 10-inch cast-iron skillet and spread out evenly. Spread the topping mixture over evenly, and then place in the center of the oven and cook until the topping is browned and the fruit is bubbling around the edges, 35 to 40 minutes. Serve with vanilla yogurt on the side.