Preheat the oven to 350°F. Lightly grease an 8" square pan or an 8" or 9" round pan., Toss the apples the salt, boiled cider, and cinnamon. Place the apples in the prepared pan, pressing them into an even layer. Set aside., In a large bowl or the bowl of a stand mixer, beat together the butter and ½ cup (99g) of the sugar until smooth and creamy; mix by hand using a flexible spatula or the flat beater attachment of the stand mixer. Add the buttermilk, flour, baking soda, baking powder, salt, and vanilla, then beat again until smooth., Spoon the batter — it should be rather stiff — over the apples in the pan, using your spatula to spread it into an even layer all the way to the edges of the pan., Sprinkle the remaining ½ cup (99g) sugar over the batter as evenly as possible. Use a small spoon to drizzle/splash the water onto the sugar, letting it soak in; the goal is to get all the sugar wet., Place the prepared apple cobbler on a baking sheet to catch any juices that may drip., Bake the apple cobbler for 35 to 40 minutes, until the surface is golden and crispy and a toothpick inserted into the center of the cake topping comes out clean., Remove the apple cobbler from the oven and place it on a rack to cool and set for about 30 minutes; the topping will settle during this time., Serve the apple cobbler warm, with or without vanilla ice cream., Cover and refrigerate any leftovers. Reheat in a warm 300°F oven for 10 to 20 minutes.