Preheat oven to 425°F. Toss together apples, brown sugar, and all-purpose flour in a large bowl. Melt 4 tablespoons of the butter in a large skillet over medium-high. Add apple mixture, and cook, stirring often, until apples are tender and syrup thickens, 20 to 25 minutes.

Meanwhile, stir together self-rising flour and 2 tablespoons of the granulated sugar in a large bowl. Cut 1/2 cup cold butter cubes into self-rising flour mixture with a pastry blender or fork until mixture is crumbly and resembles small peas; freeze 10 minutes.

Remove apples from heat; stir in lemon zest and juice, cinnamon, and salt. Spoon apple mixture into a lightly greased 8-inch square (2-quart) baking dish. Bake in preheated oven 15 minutes, placing a baking sheet on oven rack directly below dish to catch any drips.

Meanwhile, make a well in center of flour mixture. Add 3/4 cup cream; stir just until dough comes together, adding additional cream up to 1 cup, 1 tablespoon at a time, if needed. Turn dough out onto a lightly floured surface, and knead lightly 3 or 4 times. Roll or pat dough to 3/4- to 1-inch thickness. Cut with a 2 1/2-inch round cutter; reroll scraps once, and repeat process to make 9 biscuits.

Place biscuits on top of hot apple mixture in baking dish. Melt remaining 2 tablespoons butter, and brush over biscuits. Sprinkle biscuits with remaining 1 tablespoon granulated sugar. Return cobbler to oven, and bake until biscuits are golden and done, 15 to 17 minutes. Cool 30 minutes; top servings with ice cream.