
Preheat the oven to 375°F. Generously spray a 9×13 glass⁵ or ceramic pan with baking spray.
In a small heatproof bowl, melt the butter. Set aside to cool until just warm to the touch (about 75°F).
In a medium bowl, whisk together the cooled butter, buttermilk, and vanilla until combined. In a separate medium bowl, whisk together the flour, sugar, baking powder, and salt. Add the wet mixture to the dry mixture, whisking until combined and no clumps are visible. Set aside for 10 minutes to thicken.
In a large bowl, toss the blueberries with the sugar, cornstarch (if using frozen berries), lemon zest, lemon juice, cinnamon, and salt. Break up any cornstarch clumps as you mix.
Spread blueberry mixture evenly into the prepared pan. Dollop the batter evenly over the blueberries, then spread gently to cover. Sprinkle coarse sugar evenly over batter, if using.
For frozen berries: Bake uncovered for 40 minutes, then tent with foil and bake for 15–20 minutes more. For fresh berries: Tent with foil after about 25 minutes, then bake for another 25 minutes, or until done. The topping will look golden before it’s fully baked, so check several spots with a toothpick. It’s okay if there’s blueberry juice on the toothpick. If the topping still looks slightly wet, bake uncovered for 1–2 minutes more.
Let the cobbler cool until just warm before serving, about 45 minutes. The topping will be thin and lightly crisp while warm, then soften and thicken as it cools.