Preheat oven to 425ºF. Line an 11-by-17-inch rimmed baking sheet with parchment paper. Coat the parchment and sides of the pan with nonstick cooking spray. Set aside.
Whisk the buttermilk, eggs, vanilla, and 2 tablespoons melted butter in a medium bowl until combined. In a separate large bowl, whisk the flour, sugar, baking powder, baking soda, and salt. Add the milk-egg mixture and stir until just combined (do not overmix).
Scrape the batter into the prepared baking sheet, smoothing into an even layer with a spatula.
Bake until the pancake is lightly golden and springs back in the center when poked, 11 to 13 minutes. Remove from oven and heat the broiler to high. Brush the remaining 2 tablespoons melted butter onto the pancake. Broil until golden brown, 1 to 2 minutes, rotating halfway.