Preheat the oven to 375 degrees . Butter an 8-by-8-by-2-inch baking dish.
Mix the blueberries with 1/3 cup of the sugar and 2 tablespoons of the flour. Spoon into the baking dish.
In a large bowl, whisk together the remaining 1 1/2 cups of flour and 3 tablespoons of sugar with the baking powder and salt. Cut the butter into the flour mixture with a pastry blender or 2 knives until it resembles coarse meal. Add the milk and vanilla and stir with a fork to form a wet, sticky dough. Drop rounded teaspoons of the dough over the top of the blueberries to cover them. Sprinkle the remaining 1 tablespoon of sugar on top of the cobbler and place the baking dish on the middle rack of the oven. (Place aluminum foil on the rack directly below the cobbler to catch any juices that might spill over.) Bake for 45 minutes, or until the top is golden-brown and the fruit filling is bubbling up through the crust.
Let the cobbler cool for at least 20 minutes. Serve warm or at room temperature.