In a medium pot, melt ¼ cup of butter over medium heat. Add apples and toss in the butter to coat. Add lemon juice, brown sugar and salt and stir to combine. Continue cooking over medium low, stirring occasionally, until the sugar dissolves and the apples start to soften, about 5 minutes. Remove from heat and stir in flour until the mixture thickens.
Heat oven to 400°F. Lightly grease a well seasoned 9" cast iron skillet or glass or ceramic baking dish with remaining tablespoon of butter. Transfer the apple filling into the prepared pan.
In a medium bowl, whisk the flour, baking powder and salt together to combine. Add the cold, cubed butter and toss to coat in flour. Then use a pastry cutter, a fork or your hands to cut the butter into the flour until the mixture resembles a coarse meal with small, pea sized granules. Add about ¾ cup of the grated cheddar cheese, setting aside ¼ cup, and cut the cheese in with a pastry blender or a fork, just until combined. The dough should be shaggy with visible cheese shreds.
Make a well in the center of the bowl and pour in the buttermilk. Use a fork to mix all the ingredients together until just combined.
Using a tablespoon, scoop about 12 mounds of biscuit dough and drop the dollops over the apple filling. It should cover most of the surface, however, some of the filling will still be visible between the biscuits. Top the biscuits with remaining shredded cheese.
Transfer to the oven and bake for 15 minutes at 400°F. Then turn the temperature down to 375°F and bake for another 30-ish minutes, until the filling is bubbly and the biscuit topping is golden brown. Cool at least 15 minutes and serve warm.
