Line a baking sheet with parchment paper.
In a large bowl, whisk together flour, sugar, baking powder, and salt. Using a pastry cutter or a fork, cut in the cold butter until the mixture resembles coarse crumbs; this should take only a minute or two thanks to the grated butter. Add the shredded cheddar, diced apple, and chopped rosemary and toss until the cheese and apple pieces are well coated with flour.
In a separate bowl, whisk together the eggs and heavy cream. Add this to the dry ingredients, stirring until just combined (I like to use a fork). There may be pockets of dry flour and that is normal.
Turn the dough out onto a lightly floured surface and gently knead until it just comes together; it should still appear a little shaggy, not smooth. Handle it as little as possible. Form the dough into an 8-inch circle, about 1 inch thick. Cut the circle into 8 wedges. (For smaller scones, divide the dough in half and form each half into a small circle about 1 inch thick; cut each circle into 8 wedges.)
Brush the tops with a light coating of heavy cream, then sprinkle with coarse sea salt. (If you're not baking these right away, save this step for later.)
If your fridge is big enough to accommodate a baking sheet, transfer the scones to your prepared baking sheet, leaving as much space as possible between each scone for air circulation. If your fridge cannot fit a sheet pan, transfer the scones to a plate for now.
Refrigerate the scones while the oven preheats to 400°F; at least 15 minutes. (This ensures the butter stays cold and that the scones keep their shape as they bake.)
Once the oven is hot, transfer the scones to a prepared baking sheet if needed. Bake large scones for 20-22 minutes, or until golden brown around the edges. Bake small scones for 18-20 minutes.
Allow to cool on the baking sheet for 5 minutes before transferring to a wire rack. These are the best when served warm!