Heat the oven: Preheat to 350°F (175°C). Place the butter in a 9x13-inch baking dish or a 10-inch ovenproof skillet. Slide it into the oven to melt while it heats.
Keep an eye on it so it doesn’t brown.
Prep the blueberries: In a bowl, toss the blueberries with 1/4 cup of the sugar. If your berries are very tart, you can add an extra tablespoon of sugar. Set aside.
Make the batter: In a separate bowl, whisk the flour and remaining 3/4 cup sugar.
Add the milk and whisk until smooth. If using, stir in a pinch of salt and vanilla.
Build the cobbler: Remove the dish with melted butter from the oven. Pour the batter directly over the butter—do not stir.
Spoon the sugared blueberries evenly over the batter. Again, do not stir. The batter will rise around the fruit as it bakes.
Bake: Return the dish to the oven and bake for 40–50 minutes, until the top is golden brown and set, and the edges are bubbly.
If using frozen berries, it may need an extra 5–10 minutes.
Rest and serve: Let it cool for 10–15 minutes so the juices thicken slightly. Serve warm with vanilla ice cream or whipped cream.