Preheat oven to 350°F (175°C). Pour the melted butter into the bottom of a 9x13-inch baking dish. In a separate bowl, whisk together the flour, baking powder, salt, granulated sugar, milk, and vanilla extract until smooth. Pour the batter over the melted butter—do not stir.
Sprinkle the brown sugar evenly over the batter. Then, scatter the chopped pecans over the top. Again, do not mix—this layering is what gives the cobbler its gooey filling and crisp top.
Carefully pour the boiling water over the entire dish. This might seem strange, but it’s key to creating that caramel-like sauce as the cobbler bakes. Don’t stir.
Place the baking dish in the preheated oven and bake for 40–45 minutes, or until the top is golden brown and set. The bottom will be soft and gooey. Let cool slightly before serving.