Preheat an oven to 350F. Place ¼ cup (55g) unsalted butter in a 10-inch cast-iron skillet, then place in the oven to melt for about 5 minutes. Remove from the heat and set aside.
In a large mixing bowl, combine sliced apples, brown sugar, sugar, lemon juice, cornstarch, ground cinnamon, and kosher salt. Toss to thoroughly coat, then carefully pour into the cast-iron skillet. Bake.
In a separate bowl, whisk together all-purpose flour, sugar, baking powder, cinnamon, and kosher salt. Add cubed cold butter, then work it into the flour mixture with a pastry cutter (or your hands) until the butter is the size of small peas. Pour in heavy cream or milk and vanilla.
Carefully remove the skillet from the oven then use a large cookie scoop to dollop the batter over the filling. Brush the batter with remaining heavy cream, then sprinkle with turbinado sugar. Immediately sprinkle with a pinch or two of flaky sea salt.
Combine heavy cream, confectioners sugar, vanilla extract, and cinnamon in the bowl of a stand mixer fitted with whisk attachment. Whip until stiff peaks form. Serve the apple cobbler warm with whipped cream!