Preheat the oven to 425 degrees F.
Lightly grease an 8-inch square baking dish with the extra butter.
In a large bowl, add the Granny Smith apples, the Braeburn apples, the brown sugar, and 4 tablespoons of the all-purpose flour and toss until the apples are well-coated.
In a large skillet over medium-high heat, melt 4 tablespoons of the butter.
Add the coated apples to the skillet and cook, stirring often, until the apples are tender and the syrup thickens, about 20-25 minutes.
Transfer the apples from the heat and add the lemon zest, the lemon juice, the cinnamon, and the salt, stirring to combine.
Spoon the apple mixture into the prepared baking dish.
Bake the apples, placing a baking sheet under the baking dish to catch any drippings, for 15 minutes.
Transfer the apples from the oven and set them aside.
In a large bowl, add the self-rising flour and 2 tablespoons of the granulated sugar and stir together.
Add 1/2 cup of the cold butter cubes into the self-rising flour mixture and cut with a pastry blender, until the mixture crumbles and resembles small peas.
Place the flour-butter mixture into the freezer until firmed up, about 10 minutes.
Make a well in the center of the flour mixture and add 3/4 cup of the cream to the well, stirring just until the dough comes together. Add the remaining cream as needed, 1 tablespoon at a time, to make sure the dough comes together.
Using the extra all-purpose flour, lightly dust a work surface.
Turn the dough out onto the prepared work surface, and knead lightly 3-4 times.
Roll or pat the dough to 3/4-1-inch thickness and cut it with a 2 1/2-inch round cutter to make as many circles as possible.
Reroll the remaining dough and repeat the rolling and cutting process until 9 biscuits are made.
Place the biscuits on top of the hot apple mixture in the baking dish.
Melt the remaining butter and brush it over the biscuits.
Sprinkle the biscuits with the remaining granulated sugar.
Return the baking dish to the oven and bake until the biscuits are golden and firm, about 15-17 minutes.
Transfer the bake from the oven and let cool, about 30 minutes.
Serve, topped with the ice cream.