Preheat the oven to 375˚F (190˚C) and lightly grease your baking dish.
Prepare the filling: in a large bowl toss all the ingredients for the filling: fresh blackberries, diced pear, berry jam, zest and lemon juice, vanilla, rum, cinnamon, and salt, and mix well. Pour the filling into the prepared dish, and let sit for 10-15 minutes to let the juices start flowing.
Prepare the biscuit topping: in a mixing bowl combine the flour and the diced butter. Cut the butter with a pastry cutter into the flour, or if you don't have one, gently rub the butter and flour between your fingers, until you break it into smaller pieces. Then rub the between the palms of your hands until you get a grainy, sandy texture. Add the sugar, baking powder, salt, vanilla, and oats. Mix well and stir in the milk. If you prefer a drier, crunchier topping, make sure your dough is not too soft and it holds well together (like in the photos). If you prefer a more cake-like topping, add more milk to soften your dough. Either way, the topping will taste delicious.
Assemble the cobbler: using your hands, break pieces of dough (around 2 inches) and scatter them evenly all over your blackberry filling. If you made your dough a bit more wet, use two spoons to dollop your topping.
Bake the cobbler: bake your Fresh Blackberry Cobbler for 35 minutes. Make sure to check after 25 minutes, depending on your oven. If you want your topping to be a bit crunchier, sprinkle now some brown sugar on top, and cook for 15 more minutes, or until the crust is golden brown.
Serve as is, or with a scoop of ice cream or some whipped cream.