Preheat the oven to 350°F. Lightly grease a 9×13-inch baking dish.
In a small saucepan, melt the ½ cup butter over medium heat.
Continue cooking, swirling often, until golden brown specks form and it smells nutty (5–7 minutes).
Set aside to cool slightly.
In a mixing bowl, whisk together flour, sugar, baking powder, and salt.
Stir in milk until smooth.
Slowly whisk in the cooled brown butter until combined.
Pour this batter evenly into the prepared baking dish.
In a separate bowl, whisk together brown sugar, eggs, corn syrup, and vanilla.
Stir in the pecans.
Gently spoon this mixture over the batter in the dish (don’t stir — the layers will bake into each other).
In a small saucepan, heat maple syrup and butter until bubbling (2–3 minutes).
Stir in cream and a pinch of salt; simmer briefly until slightly thickened.
Drizzle over the pecan mixture and gently swirl with a knife for ribbons of caramel throughout.
Mix the turbinado sugar, cinnamon, and nutmeg.
Sprinkle evenly across the top.
Bake for 40–45 minutes, until the center is just set and the top is golden. The cobbler should be slightly gooey in the middle.
Let cool for at least 20 minutes before scooping.
Serve warm with whipped cream or vanilla ice cream.