Peel all the potatoes and, as you peel them, put them in a large container with 1 gallon water and the lemon juice to keep them from browning. Once they are all peeled, remove them from the water and pat dry. Then slice the potatoes about 1/4-inch apart and about three-quarters of the way through to create a series of uniform slices so that they are still joined together at the bottom. This should create a fan type finish to the potatoes.
Next, using a whisk, blend the butter, parsley, salt and pepper. Make sure to mix well. Dunk the potatoes into the butter mixture, making sure that the slits in the potato soak up the mixture as well. Place the potatoes on a baking sheet and bake for 30 minutes.
After 30 minutes, remove the potatoes, re-heat any remaining butter and drizzle on top. Divide the cheese mixture over the potatoes. Bake the potatoes until the cheese is melted and the potatoes are cooked through, about 15 minutes. Once melted, remove the potatoes and serve.