Spray a 10-inch cast-iron skillet with nonstick cooking spray. Add pecans, 1/2 cup butter, brown sugar, maple syrup, and salt. Cook over medium heat until butter melts and sugar is dissolved, stirring occasionally. Remove from heat.
In a medium bowl, whisk together flour, sugar, baking powder, salt, and baking soda. In another medium bowl, whisk together buttermilk, melted (6 Tbsp) butter, vanilla, and eggs. Add to flour mixture, stirring until smooth. Gently spoon batter over pecan mixture in skillet. (Do not stir.)
Bake until golden brown, and a wooden pick inserted in center comes out clean, 20 to 25 minutes.
Remove from oven. Let stand in pan 10 minutes. Place a flat serving plate over cake; carefully invert cake onto plate. Spoon any remaining pecan mixture in skillet over cake.