"the cheese is something you eat with the apple pie, like a lump of ice cream,"

I'm not sure what it would taste like with Cheddar but with a nice mild, creamy, crumbly cheese like Wensleydale or Cheshire - or a good farmhouse Lancashire - it's a delight. Those cheeses are also good with a nice fresh apple or a piece of moist fruitcake. It's pretty much an institution here in Yorkshire.