Preheat the oven to 400F. Line a 6-inch cast-iron skillet with parchment paper on the bottom. Spray the parchment paper and sides of the skillet with cooking spray.
In a medium bowl, toss peaches with lemon juice, flour, sugar, and cinnamon until combined. Pour into the skillet and arrange in an even layer.
In another medium bowl, mix flour, baking powder, sugar, and salt. Add the butter and toss to coat the butter completely with the flour. Take each cube of butter and smash it between your fingers. Continue breaking up the smashed butter into the flour until the butter is the size of peas. Slowly pour in the buttermilk and almond extract, and mix until combined. The batter will be wet and sticky.
Scoop a 2-inch chunk of the batter with a spoon, then use your fingers to gently drop the batter on top of the peaches. Repeat, spooning the batter and dropping onto the peaches in an even layer. Sprinkle the sections of batter with turbinado sugar.
Place the skillet on top of a large baking sheet (this will prevent any juices from dripping in the oven).
Bake in the oven for 30 to 40 minutes or until the peaches are somewhat broken down, thick, syrupy, and bubbling and the biscuit topping is dry with a deep golden-brown color.
Meanwhile, whip heavy cream to soft peaks, then whisk in the skyr and as much powdered sugar as desired. Keep in the fridge until ready to serve.
Remove from the skillet from the oven and let cool on a wire rack for 10 to 15 minutes before serving. Serve peach cobbler with a generous dollop of skyr cream on top.