Prep the peaches: In a medium saucepan, combine the sliced peaches, 3/4 cup sugar, and 1/4 teaspoon salt. Stir to coat every slice. Cook over medium heat for 3 to 4 minutes, just until the sugar dissolves and the peaches release their juice. The liquid should look syrupy, not watery. Remove the pan from the heat and set it aside.
Heat the oven and melt the butter: Preheat your oven to 350°F. Place the 6 tablespoons of butter in the 9x13 dish and slide it into the oven. Let it melt completely, about 5 minutes. When you take it out, the butter should be sizzling — not just melted, but actively bubbling.
Mix the batter: In a large bowl, whisk together the flour, 1 cup sugar, 2 teaspoons baking powder, and 1/4 teaspoon salt. Pour in the 3/4 cup milk and stir until just combined. A few lumps are completely fine. Overmixing at this stage develops gluten and makes the crust tough.
Assemble the cobbler: Take the hot dish with the melted butter out of the oven. Carefully pour the batter directly over the butter. Do not stir. It will look strange and separate — that's the point. Spoon the peaches and all of their syrupy juice evenly over the top of the batter. Sprinkle cinnamon generously over everything.
Bake: Place the dish in the oven and bake for 38 to 40 minutes. The top should be a deep golden brown, and the peach juice should be bubbling thickly around the edges. A toothpick inserted into the crust (not the fruit) should come out clean.
Cool briefly: Set the dish on a wire rack and let it cool for 10 minutes. This step is crucial — it lets the juices settle and thicken so you don't end up with a puddle on your plate.
Serve: Scoop it warm, preferably with a scoop of vanilla ice cream melting into the top.