Melt 3 tablespoons butter in a 10-inch cast iron skillet over medium heat; remove from heat and set aside.
In a large mixing bowl, using a mixer on medium speed, beat eggs, buttermilk, brown sugar and vanilla until well combined – about 1-2 minutes. Beat in flour until just combined. Pour egg mixture into skillet. Bake 15-20 minutes or until well risen and golden brown.
Meanwhile, prepare the praline sauce by cooking pecans in a medium saucepan, over medium heat, stirring frequently, until toasted and fragrant – about 2 minutes. Stir in additional 1 tablespoon butter, sweetened condensed milk, maple syrup, cinnamon and salt until well combined.
Slice Dutch baby pancake into wedges and place on plates. Top with peach slices and drizzle with praline sauce.