Spread the peach slices in the bottom of a 10 or 12 inch cast iron skillet. Dollop 4 tablespoons of the butter overtop. Toss the sugar and cinnamon together and sprinkle half over the peaches.
Set the skillet in the oven to 6-8 minutes until the butter browns and is very fragrant.
While the buttered peaches cook, prepare the batter. Melt the remaining 2 tablespoons of butter in the microwave for 30 seconds. In a stand mixer or with a hand mixer, beat the eggs for one minute, then add in the flour, milk, butter, vanilla, and salt and beat on high speed for an additional minute until no visible clumps of flour remain.
Remove the skillet from the oven and immediately pour the batter into the hot pan. Sprinkle with cinnamon sugar. Return to the oven for 18-20 minutes longer. DO NOT OPEN THE OVEN DOOR THE FIRST 15 MINUTES OR YOUR PANCAKE WILL FLATTEN LIKE AN ATROPHIED ASS. The pancake should climb up the edges of the skillet and puff up in the middle.
Serve the Dutch baby warm with powdered sugar, maple syrup, and fresh peach slices, as desired.