Preheat oven to 350°F. While oven is preheating, place the butter in a 9x13-inch baking dish and place the pan in the oven so the butter can melt as the oven is warming.
Whisk flour, granulated sugar, baking powder and salt in a medium sized bowl. Whisk in milk and vanilla extract.
Once butter is melted, carefully remove hot pan from the oven. Drop spoonfuls of the flour mixture evenly all over the melted butter.
Sprinkle the chopped pecans over the top of the batter, then sprinkle the brown sugar evenly over the pecans.
Carefully pour the boiling water evenly over the top of the cobbler.
Place the cobbler back in the oven and bake until the cobbler is golden brown all over, about 25-35 minutes.
Cool slightly before serving. Store loosely covered for up to 2 days on the counter or 3 days in the refrigerator.
Serve hot, warm, or room temperature with whipped cream, ice cream or plain.