Preheat oven to 400°F.
Cut butter into 1" pieces and chill well in the fridge. Measure buttermilk and place in the fridge. Leave both in fridge right up until ready to use to keep them as cold as possible.
Combine pastry flour, salt, baking powder, and cheddar cheese in a medium mixing bowl. Toss well to combine and coat cheese in flour.
Add butter cubes to dry ingredients and toss to coat. Pinch and rub butter pieces into the flour between your finger tips until they're the size of small grapes. Work quickly so the warmth of your fingers doesn't start to melt the butter.
Add cold buttermilk and fold gently with a spatula just until combined. It's okay if there's still some dry floury bits left in the bowl.
Turn dough out onto lightly floured countertop or cutting board. Use your hands to roughly shape the mixture into a flat rectangle shape. Then use a bench scraper to cut through the dough in a cross hatch pattern.It won't hold together yet, that's okay. Gather the dough into a rough rectangle about ½" tall. Use the bench scraper to fold the rectangle in thirds like a letter.Then slide the bench scraper under the dough packet, lift it up, and rotate it 90 degrees on the counter. Flatten the dough rectangle out again so it's about ½" tall and longer than it is wide. Use the bench scraper to straighten the sides and ends of the rectangle as best you can. Repeat the letter fold process and rotate the dough 90 degrees again.The dough should be holding together much better at this point.
Flatten the dough out into a 5x5" square about 1" tall. Use the bench scraper in an up-and-down motion (don't saw or slice) to trim the edges (remove as little as you can) all the way around so you have a sharp square and can see the layers inside.
Press the scraps gently into the top of the dough square, then divide the dough into four equal sized pieces, again using the bench scraper in an up-and-down motion.
Transfer biscuits to lined sheet pan and brush just the tops with egg wash. Sprinkle with flaky salt. If the dough seems to be getting soft or warm, place in the fridge for 10-15 minutes prior to baking.
Bake for 20-22 minutes at 400°F until shiny and golden brown on top.