Preheat your oven to 375°F. Pit and chop the plums into a small dice.
Combine the blueberries and plums in a bowl with 1/2 cup of brown sugar (2.8 ounces), cornstarch, and cinnamon. Mix well and pour into a 9 inch pie plate or 8 x 8 baking dish.
Melt butter and set aside to cool slightly.
Combine flour, baking powder, salt, oats, and remaining brown sugar in a separate bowl, whisk to combine.
Lightly beat egg and pour into flour mixture, work it in with a fork or your fingers until the flour mixture looks like coarse crumbs.
Spread the flour mixture evenly over the fruit filling. Add the vanilla into the melted butter and pour over the cobbler topping.
Bake for 35 minutes, or until top is a rich golden brown and the fruit filling is bubbling.
Allow to cool for 10 to 20 minutes before serving. Store at room temperature, covered, for up to 3 days.