Preheat the oven to 375°F.
Prepare an 8x8x2-inch baking dish by coating with butter.
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 ½ cups of flour with 3 tablespoons of sugar, 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 teaspoon-sized dollops 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. Tip: line the rack below with aluminum foil to catch any drips during the baking cycle. Bake for 45 minutes, or until the top is golden-brown and the fruit filling is bubbling up through the crust.
Remove from oven and allow cooling for 20 minutes. Serve warm or at room temperature.